Bum-bo the Brave is definitely the most simple character in the game, which makes sense as he is the one you start out with.

Starting attack
His starting attack does a high 3 damage to a single enemy, but it costs 4 white mana to cast.

Starting spell
His starting spell costs 2 black mana and rerolls the board, and should be used when you want to try your luck with a better board or when you desperately need a combo at the end of your turn.

Unique effect
He does higher damage at lower health, which is a nice bonus but really shouldn't be relied on. Both his puzzle and spell damage will increase by 1 for each full heart of damage he takes, and this effect even persists until the end of the floor if you manage to heal the damage back (I believe, not positive).

Trinket / item strategy
Offensive: An effective but unreliable strategy is to focus completely on offense, picking up cost reduction and damage up needles as well as choosing spells and trinkets that provide additional attacks or effects granted by attacking. Such trinkets can have a chance to give you energy on attack or give you life steal on kill, which are both amazing for helping Bum-bo the Brave make up for his lack of defense. Others can give soul hearts from attacking or add wild cards on kills, which are also useful.
Defensive: Another option is to pick defensive spells and trinkets and diversify your spells' mana types, which is a more strategic and less brute-force approach. While the brute force approach will likely work wonders for just unlocking Bum-bo the Swift, if you choose to play Bum-bo the Brave after you've unlocked a few more zones, then the defensive approach is more reliable.

Gameplay strategy
Not much to say here. Pay attention to the mechanics of enemies and bosses, learn how to manipulate the board and plan ahead, and try not to die. Kill enemies with your attacks and shuffle the board when it's lacking and / or filled with curse tiles, and try to block primed enemies with boogers and poop. Bum-bo the Brave's playstyle is very vanilla, which is likely intentional as it allows you to focus more on learning the game which will be useful for the later more unique characters. His unique effect will likely see some use no matter how hard you try as he has no real way to entirely keep from taking damage, but the resulting high increase in damage should help you smash whatever's causing you trouble. Not a bad character but not particularly strong either.

Bum-bo the Nimble is a jarring change of pace from Bum-bo the Brave, requiring much more strategy with no real way to brute force through to the next unlock. He's honestly one of the harder characters in the early game, takes time and luck to get a good setup with him.

Starting attack
His damaging spell now costs 4 yellow mana to cast, and starts at a low 1 damage but has the unique effect of ganing damage with each hit. It will gain 1 damage each time you attack an enemy with it, but will reset back to 1 damage upon entering the next room. Adding damage up needles to it will increase the starting damage to 2 and each hit will still add 1 damage.

Starting spell
His other spell seems particularly weak compared to Bum-bo the Brave's board shuffle for the same cost of 2 black mana, but it can actually be stronger in the right hands. It lets you select one tile to remove from the board, and you will gain one mana equal to its type (green tile = +1 green mana, etc). Selecting a heart tile, curse tile, or wild card will not give you any mana.

Unique effect
Bum-bo the Nimble is where you must start to learn to manipulate the board to your advantage to succeed. His unique effect allows him to gain 1 of each mana from puzzle attacks (just bones and teeth) which remains constant regardless of how big the black tile combo was (though obviously it will give 2 of each mana if you get a 5 white combo and throw 2 bones).

Trinket / item strategy
As far as spells go you're going to want to prioritize ones which require white and green mana to cast to make full use of his unique effect, and defensive trinkets or ones that give you more movement/mana are helpful, as are additional attacks and spells that manipulate the board. A way to significantly boost the effectiveness of his starting attack is to get 2 cost reduction needles on it and some damage up needles as well, making it cost only 2 yellow mana. This will allow you to attack twice per 4 yellow tile combo, and attack once after you throw 2 puzzle attacks / destroy 2 yellow tiles with your second spell. In addition, try the stat wheel for puzzle damage ups and movement ups which will help significantly, as well as luck ups which will make crits more useful.

Gameplay strategy
As far as gameplay, you should always be paying attention to the tiles above the board, in order to make effective use of your tile removal spell. Its main use will be setting up combos, but always pay attention to which tile type you're removing as you'll gain mana of that type. You want to pretty much spam teeth and bones for mana and damage against smaller enemies, and save your spell attack(s) for bigger enemies. Priority of combos should be yellow > black > white > everything else, unless you need to defend against attacks. You will likely struggle and take a few hits in the early game, but you can reliably build a very strong run with needles and stat ups, as well as some helpful spells and trinkets.

Bum-bo the Stout is definitely the strongest of the characters thus far.

Starting attack
His starting abilities costing brown and green mana allows him to focus on both defense and offense at the same time, and tear through any tiles he doesn't like. His starting attack does 2 damage and knocks whatever you hit back.

Starting spell
His second ability will remove a tile and the 4 cardinally adjacent to it, and if it is used on an edge it won't wrap around. You can try to be clever with this and try to line up combos and stuff, but I find it's most effective if you just use it to get more brown tiles on the board.

Unique effect
His unique effect is that he gains 1.5x the amount of mana from the board, but he loses all of his mana after every turn. While this may sound like a huge downside, it's actually what makes him so overpowered. Setting up a simple 4 brown tile combo nets you a 1 hp poop, as well as 2 separate 2 damage attacks, for a cost of as low as 1 movement. Setting up a 4 green tile combo allows you to stun an enemy and remove 10 tiles that you don't want, for a cost of as low as 1 movement.

Trinket / item strategy
What's even more overpowered is that both of his spells only cost 3 mana, so if you are able to reduce their cost by 1 you can increase this absurdity to 3 2 damage attacks per brown tile combo and the removal of 15 tiles per green tile combo, which is just ludicrous. Add ontop of that the ease with which you can get a spell damage up from the shop, allowing you to turn your 4-6 damage per combo into 6-9. Try to prioritize spells that diversify your mana costs, specifically ones that manipulate the board, attacks, and ones that cost yellow mana. Trinkets that give you movement will be especially useful since you lose all of your mana after your turn, such as the hoof which gives an additional movement for the first turn of every room or the one that has a chance to give movement on each attack, which procs incredibly often when you're attacking 3+ times a turn. Specific spells that I used to steamroll the third chapter were the poison attack, the AoE furthest enemy attack, the 'turn any tile into a wild card' for 4 yellow mana spell, the spell which gives you mana = to the most common tile on the board (paper straw I believe), and the d8 which is a charge item that switches around your mana numbers for 0 charge (but can only be used once per turn). It should be noted that using items like the d8 or the paper straw when you have no movement has the chance to end your turn, which isn't ideal.

Gameplay strategy
As far as gameplay you're pretty much going to want to focus getting brown and yellow tile combos for your OP attack and a longer turn, as well as getting green tile combos to destroy the board and fill it up with more brown tiles so you can do the same the next turn. It's helpful to clear out columns so that you can stack up poop and boogers on one or two columns without having to worry about attacks from all 3. The third zone is substantially more difficult than both of the 2 zones before it, so be prepared for that. That's really the only place you're going to be dying as Bum-bo the Stout, unless you get an unlucky start to your run. Otherwise, have fun playing this OP character and unlocking the next one.

Bum-bo the Weird is certainly the most unique of the characters thus far.

Starting attack
His starting attack spell costs 3 white mana and 3 black mana, which is very expensive. However it is also very powerful - it lets you select a tile type on the board, which it then completely removes, and then does damage based on the amount of tiles consumed (amount of tiles / 2 rounding up. So if for example there are 7 green tiles on the board, it will remove all of them and deal 4 damage to whatever enemy you select). Reducing its cost once will make it cost 2 white mana and 3 black mana which is more manageable, though adding spell damage to it doesn’t seem to have an effect (at least not on the first one, unless it increases the potential max damage which isn’t useful anyway since you’ll rarely see 13 of one tile at a time). It can also be used to consume curse tiles, though this is a very expensive way to get rid of them unless there are a lot. It does not consume any wild cards on the board unless you select a wild card, in which case it will consume only the wild cards for no bonus damage. Gaining increased spell damage through the stat wheel or other means will only increase the potential max damage, and won't increase the starting damage at all (if you match 13+ tiles you can now do 7 damage instead of only 6).

Starting spell
His second starting spell costs 4 yellow mana and lets you select a tile type to add more of to the board, replacing ~3-6 other tiles with that tile type seemingly randomly. This does work with hearts but I haven’t tried it with wilds, and I assume it works with curses as well (which is a bad idea unless you have the black magic trinket / other curse synergies I don’t know about). A way to virtually break the game is to put 1 or 2 spell cost reduction needles on this, which can allow you to potentially clear each room in a single turn after just one yellow tile combo.

Unique effect
His unique effect is that he gains a movement for every kill, allowing you to have very long turns and potentially complete rooms without the enemies ever getting a turn.

Trinket / item strategy
For trinkets, the one that adds more yellow tiles is fairly useful, and for spells ones that cost yellow mana and green / brown mana will be good. His starting attack is very strong so try to focus on defensive spells or ones that manipulate the board, as well as good charge items. However, Bum-bo the Wise does struggle in areas where he can’t get a lot of kills such as bosses and areas with high health enemies, so be prepared for that. His starting health is very low so try to get that up if you can, as well as puzzle damage which will be useful for the high amount of bones and teeth you’ll be making.

Gameplay strategy
As for gameplay strategy, prioritize yellow combos first as these will allow you to make more black and white tiles with your second spell. Afterwards try to make an equal amount of black and white combos to fuel your starting attack and use it to get rid of the less useful tiles like greens and browns, or yellows if you’re near the end of the room. Don’t be afraid to use 2 movement to make a black / white combo if you know you’re going to be able to get a kill with it, as you’ll get a movement back for doing so. Look ahead as much as you can to try to keep your turn going, and set up poop / use boogers if you know there’s attacking enemies you won’t be able to deal with that turn. Play smart and play safe and you should be able to win fairly easily, as Bum-bo the Wise is a pretty strong character. Some mentionable boss interactions I came across are that peep is a particularly difficult first boss because you can’t get any movement from kills, and for the boss with the 3 masks that curses you when you hit the wrong one you will get movement from hitting the wrong mask so that makes it fairly easy.

The Blue Baby of The Legend of Bum-bo, by far the most uniquely challenging character so far. Expect your runs to be very long with this one.

Starting attack
Attack fly: costs 4 mana, does one damage initially and 1 damage at the start of every turn. Important to note that using this in the same lane more than once will not increase the damage over time done from 1 to 2, it will only provide the initial 1 damage and keep the 1 damage per turn afterwards (so if you only care about the damage over time, no need to cast this more than 3 times per room).This can occasionally be good, but honestly most of the time it's really bad, and is the only starting attack thus far that I'd recommend trading for something better. You can't reduce its cost and you can't add damage to it, it procs all the possible negative effects that can come from attacking something (gas clouds, swapping the puzzle/spell damage resistant enemies, etc.) and if you use it on the boss fight with the skeleton that has the red ghost inside of him your run is over (unless you somehow manage to survive 18 rounds of curses and almost unavoidable damage.) Most if not all of your damage with Bum-bo the Dead will come from puzzle attacks or other spells.

Starting spells
Buzz Right: costs one mana and lets you move a row of tiles one to the right
Buzz Down: costs one mana and lets you move a column of tiles one down
These will be your main way of manipulating the board. They seem incredibly underwhelming, and for every other character they are, but for Bum-bo the Dead they are a vital part of his gameplay, so don't trade them away. The reason for this is that he starts with a seemingly crippling 1 movement, and I'm fairly sure is limited to 1 movement for the entirety of the run. In addition, he starts every room with 2 of each mana, and he's able to use his unique effect to get extensive use out of these if you pay attention to your combos.

Unique effects
Like Blue Baby, he starts with 3 soul hearts and can only ever gain soul hearts for additional health. This is part of what makes him challenging, but his other effect is what makes him unique. Every time Bum-bo the Dead uses a spell, the mana requirement for that spell is shuffled. Keep in mind that this will never change the net cost of the spell, but only the mana types that are required (ex: if something costs 6 boogers it might change to 6 bones, or 3 bones and 3 teeth, but it will always cost 6 mana). An unfortunate but necessary downside to Bum-bo the Dead is that his shops will never have spell cost decreases, as that would allow him to infinitely manipulate the board for free. This however is partially negated by him starting each room with 2 of each mana type. Seems to be limited to his starting 1 movement, without the ability to gain movement upgrades from the stat wheel or items that give you stat upgrades (not confirmed, though I experienced this with both of the 2 runs I played with him).

Trinket / item strategy
Bum-bo the Dead can only get soul hearts, so the relic (charge item grants a soul heart every 3 turns)is extremely valuable. Another great trinket is the 9-volt (chance to gain a charge when casting a spell) which works especially well with Bum-bo the Dead considering how often you'll be casting spells. Combine these two trinkets together to virtually be unstoppable, as long as you play smart. You're also going to want to pick up some attack spells to augment / replace your starting attack, and the mana cost for any spell you choose doesn't matter as it'll get shuffled anyway. A very good replacement for his starting attack is the hook attack that costs 2 mana and gives you mana on attack, for obvious reasons (attack -> mana -> attack again). This works especially well if you add damage to it, which actually works unlike adding it to his attack fly.

Gameplay strategy
Bum-bo the Dead's gameplay is unique in that it's very much up to the whim of the board as far as what you're doing at any given time, much more so than any other character. Because the mana costs of spells are constantly changing, you're going to want to try to always have a supply of every kind of mana all the time. this can be difficult to get used to at first, but a basic strategy is to try to combo whatever mana your attack fly needs first so you can get some damage over time going, and then try to keep all of the types from hitting zero while also attacking enemies and defending their attacks as needed. Bum-bo the Dead starts with a strong 2 puzzle damage to make up for his weak starting attack spell, and this will allow you to just barely pick off key targets while holding off the rest with poop and boogers. Once you have a surplus of mana don't be afraid to spend 4 to hit an enemy with your attack fly for 1 damage, and you'll be practically forced to do this in the later zones with the aforementioned swapping spell / puzzle damage resistant enemies. Try to only use your 1 movement for very large moves that would take a lot of buzz casts to make up, and pay close attention to the many ways you can make combos instead of just the most obvious one. Since virtually all of Bum-bo the Dead's gameplay consists of micromanaging the match 4 game, this will be great practice for doing this with all of the other characters where it doesn't take several minutes just to make a few combos (this is why runs with him will tend to be really long). This is almost an entirely different game from any of the other characters, and it's fun and challenging in its own way. With some luck it's entirely possible to beat the whole game without taking damage and with killing each of your 4 bosses on your first turn, which is what I just did for my second completion using the upgraded hook and some lucky spell damage increases.

Not going to completely follow the established format on this one because his starting attack and starting spell are random, so there's no point in talking about them. Bum-bo the Empty is essentially the Eden of The Legend of Bum-bo, if Eden were on steroids. Expect a completely unique and challenging experience with this one, the likes of which you haven't seen before.

Bum-bo the Empty seems to always start with one starting attack and one board manipulating spell, though both of these will be random with a random mana type (same overall cost as normal but different types).

Unique effects
There are almost too many to list. His starting stats are completely random. Upon entering a new room, all of his spells will reroll to a spell of the same type (I believe there are 5 different types - attack, support, board manipulating, converter/magic, and charge, denoted by a sword, a heart, a puzzle piece, a purple swirl, and a remote respectively). In the casino, the needle seller now sells 3 trinkets/consumable items for 7 cents each (as upgrading a spell you're going to lose as soon as you enter a new room would be pointless). As far as spells found in treasure rooms, the only thing that matters is the spell type, because it will be rerolled upon entering the next room meaning you won't be able to use whatever you pick.

Item strategies
The only things you have control over as far as items go are trinkets/consumable items and spell types. Try to pick trinkets/consumable items that will be beneficial to you regardless of which spells you have. As far as spell types, I find that having 2 attack spells (so you don't softlock if one of them does no damage), 2 board manipulating spells, 1 charge item, and 1 defensive spell is a good mix, though you might want to have 2 defensive spells and 1 board manipulating spell instead. Charge items are particularly lucrative on Bum-bo the Empty because since they are rerolled every room, they will always be fully charged at the start of the room, meaning you will always be able to use them at least once per room. An effective strategy is to roll the stat wheel in every shop and hope you get good upgrades (unless there are really good trinkets), and you can keep restarting your run to get good stat rolls if you're having trouble with him.

Gameplay strategies
Pay close attention to your changing mana costs each room. Having a good knowledge of what exactly the items you get do will be essential, as you won't have much wiggle room to learn while you're trying to stay alive. Unfortunately this character is a lot more luck based than the other characters, so you will likely have a hard time no matter how well you play, but you'll also have to play very well to even have a chance at success. Having a detailed knowledge of enemy and boss mechanics will help, as well as being good at planning ahead with your board. Honestly the game was starting to feel a bit easy for me after beating it 10 times to unlock him, but he has the extreme level of challenge that finally made me lose after a 13 win streak.

Completion Unlocks
Every other character unlocks their starting items for their completions, but Bum-bo the Empty unlocks the D6 for his first completion, and I haven't gotten a second completion with him yet.

Difficulty, from easiest to hardest:
Bum-bo the Dead > Bum-bo the Weird > Bum-bo the Stout > Bum-bo the Brave > Bum-bo the Nimble > Bum-bo the Empty

Bum-bo the Dead is extremely tedious to play and you have to be somewhat careful with him, but his spells and mechanics allow him to completely avoid damage 95% of the time and finish rooms and bosses in one turn if you get just a decent spell attack and a spell damage upgrade, making him the easiest.

Bum-bo the Weird will likely take damage in the start when he lacks the power to completely avoid it, but all you need to do is put two spell cost reduction needles on his second ability, and you will be able to steamroll the rest of the game if you don't get screwed by rng, making him the second easiest.

Bum-bo the Stout also can struggle initially, but once you get 2 spell cost reduction needles on his starting attack you shouldn't have much trouble for the rest of the game. You might take some damage here and there, but if you don't get screwed by rng you'll be okay if you just focus on making up for his weak puzzle damage, making him the third easiest.

Bum-bo the Brave has the lowest ability of all the characters to avoid damage (besides Bum-bo the Empty) but he makes up for this by gaining huge free damage ups when he takes damage. 2 spell cost reduction needles on his main attack will be useful, but likely not obtained for a while. Before then as long as you get half decent stat ups, trinkets, and spells you should be fine, but you pretty much have to stay at 1.5 or 2 hearts in order to be able to clear the later rooms, meaning it's far easier to die if you get screwed by rng, making him the fourth easiest.

Bum-bo the Nimble is the only character (besides Bum-bo the Empty) that really struggles throughout the entire game. His early game can be really rough, and you'll likely find yourself just barely scraping through if you don't get lucky with the board. This problem is eased once you get 2 spell cost reduction needles on his main attack, and some spell damage up needles on his main attack will help as well. Even still you'll have to play well and get somewhat lucky to get through the game without a lot of trouble, making him the fifth easiest.

Bum-bo the Empty is the hardest character for obvious reasons, considering he is the challenge character. It's almost impossible to ensure a victory in any given run, as most of his success comes from rng. One bad roll can end your run, which isn't true for any of the other characters. You have to play extremely well or get extremely lucky to win, and even if you do play extremely well you still have to not get unlucky, making him the hardest character.

So that's all I have to say, I typed this up because I saw that there was a lack of guides for this game and thought I'd share my strategies as far as how I unlocked all of the characters. If you have any recommendations / critiques for the guide or strategies of your own feel free to share them in the comments below, and good luck in your future runs!