update Sep. 10: Done with masteries, publishing first version, will continue with other achievements when I have the time.
This guide will detail the game's unlocks and achievements, as well as useful mechanics and recommended strategies that can help getting them easier and/or faster.
There's an official wiki and it will be refereneced when applicable, but it is lacking, in particualr it has almost no coverage of achievements and strategies.
That being said, if anyone find any of the following useful and want to wikify if needed and add to wiki, they have my permission.

For many of the achievemnets below there will be suggestions to set up one or more of the following:

• Mastery, see below in this guide on requirements and how to unlock the different masteries.
  
• Special chest[demoncrawl.com], it's recommended to unlock those asap as some are very useful.
  
• Heirlooms
  
  • With the right recepies and the required artifacts, one can craft items into an available heirloom slot, once per game one can take an item from the heirloom slots into the inventory.
    
  • It's possible to craft during a quest, so for instance if two craftable items are required for a synergy, once one was found the other can be crafted.
    
  • Not all items have recepies.
    
  • There are ways to exploit the heirloom slots, see infinite crafting section below.
• Favourite items
  
  • Before a quest, in the codex section, one can favor up to 5 items. This will make the items more likely to drop (as well as their recepies if not found yet)
    
  • The max value of items that can drop from chests is limited by the stage's max power, see here[demoncrawl.com]
    
  • Shop will show items worth up to the current gold held by the player and a little more, so when trying for a specific item it's best to have enough money or it won't show in the shop
• Divine items[demoncrawl.com]
  
  • When there's no active quest, items can be toggled between the regular and divine version
    
  • Only one divine item can be held at a time (same as legendary), so having too much toggled on may not work well
• I didn't mess around much with sigils [demoncrawl.com]so no mentions here, but there may be some useful ones.

requirement - for level I/II/III discover cell with value 4/5/6 or greater
strategy - trivial

requirement - for level I/II/III complete a quest with at least 10/20/30 lives
strategy - one or more soul generating items: urn, book of love, crystal veins etc.

requirement - for level I/II/III complete a quest with at least 5/10/15 defense
strategy - one or more defense generating items: crucible, book of defense, iron sceptre etc.

requirement - for level I/II/III complete a quest with at least 20/50/100 total armor durability
strategy - get a synergy with an armor you can easily fortify. One easy example is to have waterboy medal ready in heirloom and look for bubble chestplate (40 coins base value). Once the armor is found use the medal, repopping a bubble in the waterboy's direction will raise the armor 1 point every turn.
Alternatively, divine forge hammer and/or magic hammer will double your armors' durability, so a base total armor of 25 will get to 100 after two doubles.

requirement - for level I/II/III complete a quest with at least 5/10/15 minions
strategy - plenty of minion generating items. For example, use the druid staff (craftable) with Detective mastery.

requirement - for level I/II complete a quest with at least 5/10 magic items
for level III complete a quest with at least 11 fully charged magic items
strategy - this one may be a little tricky as just opening chests may fill the invertory with passives.
Couple of helpful items here - toad will let one buy magic items from mages for 20g each, primordial gate will fill the invetory with magic items with time.

requirement - for level I/II/III complete a quest with at least 5/10/15 omens
strategy - Poison is an omen, so using the same strategy as unlocking Poisoner mastery should work (last level with heckaslug / toxic mod, use hungry plant medal before you start it to gurantee inventory space)

requirement - for level I/II/III destroy at least 10/30/100 objects usign cursed cells
strategy - This is one of the masteries where having at least level II is very useful for unlocking, so worth taking if found in Academy special stage.
In order to get to level II, dusk binder is probably the best, onyx of agony and shoulder devil are both craftable can help as well.
With level II mastery, as long as there are objects in the level one can use blood magic (level I ability) every turn, destorying one object and cursing the next, chaining the spells. This strategy with any item that increase loot drops of any kind should gurantee the level III unlock.

requirement - for level I/II/III glean at least 10/50/100 cells in a single stage
strategy - divine lantern (craftable) can help unlock this one easilly, besides being an excellent item all around. note it can be used directly on flagged cells (no need to unflag to use it)
Alternatively or if still locked, some combination and clever use of walking stick, spybug and fake mustache can get it done.

requirement - for level I/II/III kill at least 5/10/30 cells in a single stage
strategy - In order to see plenty of strangers, use Friendly chest, loudhailer or similar.
In order to kill them, use scorpion's tail, friendly fire, maniac's mask or similar.

requirement - for level I/II/III have 10/15/30 familiars
strategy - familiars can die and usually don't continue to the next stage, so not all familiar generating items fit.
For easy unlock recommended divine bugle or ritual chalk. Can also use brainwash with Detective mastery.

requirement - for level I/II/III have 10/20/30 simultaneous flares
strategy - bullet time (craftable) should make this trivial as flares will stay on screen a lot longer.

requirement - for level I/II/III beat a stage with at least 15/30/50 frozen cells.
"beat a stage" is when the "Finish!" appears and the timer stops, not when the "Finish level" is clicked (and triggers "complete a level").
strategy - cryomancy with divine lantern should work, make sure the level has enough monsters, then once it's almost done use lantern on flags touching at least two other flags.
Nitrogen may also work but will need some luck, for exmplae if there are 99 flagged monsters and one hidden cell remaining, there's a 50% change nitrogen will freeze at least 50 cells.
Having high pathfinding% may make this one harder as it may cause the level to be beaten prematurely.

requirement - for level I/II/III complete a stage with at least 15/30/50 electric cells.
strategy - I think using electro pulse after beating the level ("Finish!" appeared) and then finishing should work.
If not or alternatively, electroscope may do the trick, make sure to have more 0-cell values using (divine) mircale seed and/or reducing monsters using lyre/mjolnir.

requirement - for level I/II/III complete a quest with at least 3/5/7 status effects
strategy - Status effects usually end after their condition is met (x turns passed, armor was lost, mistake was made, etc.) so one method is to keep items with status effects and trigger those just before the quest's end.
Spatula creates nultuple neverending status effects all by itself.
This mastery should be unlocked for free while unlocking Poisoner mastery.

requirement - for level I/II/III complete a quest with at least 10/20/30 bubbles
strategy - using detective mastery II or above with any bubbling item - suds, bubble solution, waterboy medal, etc.

requirement - for level I/II/III complete a quest with at least 10/20/30 cankers
startegy - collect 10 dark hearts after completing a boss level with huskbane. This is the best strategy as you only spawn the cankers at the end, so they don't interfere with solving.
Using other cankers spawning items such as comeuppance and oitment will also work but requires more patience and skill.

requirement - for level I/II/III complete a stage with at least 10/50/100 visible monsters
strategy - magical bean with pentagram should work if stage is not too small.
Alternatively, flashbang by itself may unlock level II if there are enough monsters.
Once unlocked, using level II should be enough to get level III.

requirement - for level I/II/III complete a quest with at least 20/40/60% pathfinding
strategy - First, note that the only way to unlock level III is by using the mastery with level II unlocked as it raises the max pathfinding to 60%.
For level II using Bookworm mastery and using it to get pathfinding expertise and items should suffice.
For level III, time capsule (either normal or divine) with flying carpet will get you to 60%. Have time capsule heirloom ready, favor flying carpet, Avoid chests, get to ~50 gold and search shops for flying carpet.

requirement - for level I/II/III complete a quest with at least 100/200/300 coins
strategy - multiple ways to make gold in the game, some of the easier ones are golden goose, book of gold (especially with Bookwork mastery), hand of glory, divine watering can, merchant ring.

requirement- for level I/II/III create a 15/30/50-turn chain
strategy - I didn't verify this one, but it should work. Spring can double your chain length, so having a chain length of 13 and then using two springs is enough. Spring is cheap so favor and look for it in chests / shops, have second spring ready in heirloom slots.
Note that when chording, the value of the chorded cell is used for the chain, not the revealed cells around it.

requirement - for level I/II/III explode 3/10/20 sawblades in a quest
strategy - pacemaker with any souce of losing 1 health (burning cells, cankers) should work here.
Once level II is unlocked it can be used to get level III, as you can reuse sawblades.

requirement -
level I - complete a quest with no omens
level II - complete a hard quest with no omens
level III - complete a hard quest with no items
strategy - make sure to have a hungry plany on the last level, can be done by getting plant medal from heirlooms just before last level. Use the plany to empty inverntory just before completing the quest.

requirement - for level I/II/III bury 10/20/30 bones in a quest
strategy - use bone generating items - book of necromancy, bone baton etc.

requirement - for level I/II/III explode 100/300/800 cells in a quest
strategy - mortar is very useful for this one. Used together with battering ram for great explosions combo, or use with Detective mastery and any means to kill the monsters (dagger, sword etc.)
Not sure if 3x3 cells explosion count as 1 or 9 for this unlock, but getting this combo early enough in a quest should be good enough.

requirement - for level I/II/III complete a quest with at least 2/3/4 legendary items
strategy - I think getting godmonger is the only way to get this one. (or getting this mastery using Academy).

requirement - for level I/II/III complete a quest with at least 20/50/100 absolute morality
strategy - use god rays multiple times.

requirement - for level I/II/III complete a quest having a status effect with at least 100/500/1000 counter value
strategy - see Ghost mastery unlock strategy, it can work for other counters but it's best to unlock both together.

requirement - for level I/II/III complete 5/7/10 stages in a row without taking damage
strategy - In general, if using correct logic, there are four damage sources - bosses, omens, mods and guesses. By going for this unlock on normal difficulty on a quest different than V boss damages is eliminated, and also having less mods.
To negate guess/omen damage, this is more of a prefences thing. I like having pathfinding as it eliminates end of stage guesses. Bookwork mastery can also work as it can provide pathfinding, omen immunity and more, if lucky.
Try to always have an emergency item for guess situation, even a stick or cattle prod can be a clutch, not to mention items like divine lantern that can eliminates guess almost completely with correct use.
When having good enough build, it's worth considering not opening chests at all to avoid getting omens.

requirement - for level I/II/III activate 10/30/100 book effects in a quest
strategy - any book item with increased heart drops should get you at least to level I.
Using level I of this mastry will get you multiple books during a quest.
Remember that dark hearts are hearts and can activate books. Once the boss is dead / bubbled / frozen go for the hearts.
Book of ghosts's spookers will often drop candy which will generate more hearts etc.

requirement - for level I/II/III complete a quest with at least 2/3/4 revives
strategy - halo is an easy 3 revives. Each of godly goblet and ace of spades can be used multiple times to get 4. Nomads may sell god potions so with enough money one can buy 4.
Alternatively, use magic smoke bomb in a stage with celestial mod.

requirement -
level I/II - complete a quest with at least 5/10 poisons
level III - complete a quest with full invnetory of poisons
strategy - Easiest done when last stage have toxic or is heckaslug boss (can be known in advance by reading signs).
Make sure you have hungry plant, for example by using hungry plant medal from heirloom just before the stage, then after beating it use the plant to empty your inventory and fill it with poison.

requirement -
level I - complete a quest with 1 or less lives
level II/III - complete a quest with ectoplasm counter of at least 400/800
strategy -
For level I, use halo just before stage end. Can also use burned cells or cankers to lose life exactly to one, this works even when having high armor.
For level II/III, there are some hidden mechanics of ectoplasm:

• interacting with a stranger while being a ghost will make the stranger to flee and will add 20 to ectoplasm counter
  
• ghost can't interact with chests or shops, but can use items in inventory or get one from heirlooms.

The strategy is to use hourglass to keep doubling the counter, and donig it faster than the decreasing rate.
It helps having strangers in stage when turning into ghost, to increase the base counter before using the first double.
It also helps to have mana refill items ready to use right after the first double, as the first uses are the critical ones and you want to get them done as soon as possible.

requirement - for level I/II/III complete a quest with at least 1000/2000/3000 points
strategy - should be gained naturally, if struggling see the classic skins unlock below and follow the concepts there to increase stage scores.