I played Bullet Hell Monday like 3 years ago and got all Steam achievements there. As you may know, that game has a mission mode too, but its missions are way, way simpler - reason why I discarded the existence of Bullet Hell Monday Finale as a challenging game until I decided to try it out.
It turns out the existence of True Chapter plus some other things made it pretty much not trivial.

The worst part was that there is barely any information about this game, besides maybe obscure Discord discussions that I'm not going to go out of my way to find. And this game would really benefit from more of it, because some of those missions are more like puzzles in that you have to experiment and find the correct solution.

So I'll be trying to do my part with this guide.

First of all, a mission list. Courtesy of /u/natashige on Reddit:
Google Sheets[docs.google.com]

I will now proceed to say some general tips if you want to progress on missions more smoothly and without outright watching videos:

Before I start, a bug notice:
I used mouse for pretty much the entire game. While I was playing, I often encountered a situation where I would tab out of the game or open the Steam interface, and when coming back to the game, the ship would move in a more clumsily manner. There seems to be a bad interaction with mouse where it takes more effort to move in this scenario. This is solved with a game restart.

• Play the tutorials and understand them.
  
• When you're still going through the chapters, you will not be able to complete all missions of all levels on the go. A few of them seem to be particularly geared towards having a fully upgraded ship, even as early as chapter 1. Strange design decision but it does prepare you a bit for True Chapter.
  
• Following the previous point: if you feel like a mission is impossible at the time, just ignore it and try to keep going. The most important way to progress is to clear chapters by beating their bosses. This gives you lots of AP.
  
• That being said, do try to beat all levels at least once. Some unlocks are gated behind level completions, and you will need them.
  
• You will have the chance to buy the wide shot to use alongside laser shot. I would personally recommend you to only buy it to be able to use some of the SP mechanics and focus on fully upgrading laser shot first, the benefit is higher. For the same reason I would suggest against saving up for the other shots (15k AP lol) until you clear main chapters.
  
• Speaking of laser shot, never get rid of it, even while playing on True Chapter (except one particular mission). It's just that goated.

• True chapter will rain you with AP on every chapter beaten there, so go there if you need more.
  
• Spark and Time are by far the best SP equipment to use.
  
• At this point you should have noted that chapter 5 has a reprise of the previous chapters. Example: 506 is 109 and 110 combined, 507 is 209 and 210 combined, etc.
  Take advantage of your short-term memory and do missions for these in sequence (109-506 and so). You kinda save some time.
  
• Don't even bother buying or upgrading lock-on shot, I could barely find any usefulness for it when it comes to missions. Leave it for last when you have upgraded literally everything else.
  
• When it comes to the "don't move/don't do anything/beat things without damage or SP" missions, equipping shielding as a secondary with the starting shield activated is very strong. It's a free hit with literally no penalty.
  
• Suiciding for bombs is often a strat that is used for scoring in Bullet Hell Monday games, and this one is no different. In fact, you will need to do this to beat some missions. Plan a safe moment where you can die, and turn off autobomb in these cases because it's a waste.
  
• There are scenarios where you don't want to combine spark/barrier and time; this is because the time slow from time does not affect how long the other SP does, so you can end up with a bit of an anti-synergy. I could not tell you any example out of my mind right now, but it tends to happen on the endless levels.

Laser is pretty much a mandatory, so this section is mainly for debating what secondary weapon to bring once you have everything upgraded.

• Wide is useful at first and on some specific missions, but ends up being overclassed due to its weak bomb and, due to being too wide, not being able to get through heavy enemies.
  
• Search shot is what I would consider your best secondary, and you should default to it after it's upgraded and you're trying to figure out a route for most misssions. Being able to get most of those pesky tiny enemies that stay for 0.25 seconds is genuinely huge.
  
• Homing is a worse search, but on very specific missions where you need the missile explosions to kill stuff instantly it shines. Best example is 409 or 504.
  
• Shielding... because its strength lies in shielding you, the shot itself is weak. This should only be used if for some reason you don't need any of the other secondaries, or if going for no damage clears.
  
• Lock-on sucks. If you can find a mission where it's actually useful let me know.

Now, because I was made aware that some of these missions would be more akin to a puzzle, I decided to start recording some of them so that future players do not have to spend as much time racking their heads.

These are the missions that you'll find here, ordered by video appearance:

• 305: 100% destruction rate
  
• 309: 50 enemies with other weapons while spark, 100 enemies, 1500% score multiplier
  
• 403: 10 blue obstacles
  
• 409: 120 enemies with bombs, 110 obstacles, 2500% score multiplier
  
• 410: 8 enemies with auto-bomb
  
• 502: don't move for 30 seconds, don't do anything for 10 seconds
  
• 508: 20M score, 3500% score multiplier
  
• 509: 25M score, 4000% score multiplier
  
• 510: no-damage, bombs nor SP clear
  
• 109': 10M score
  
• 110': No damage nor bombs
  
• 206': 100% destruction rate
  
• 207': 100% destruction rate
  
• 208': 100% destruction rate
  
• 209': 10M score
  
• 210': 20M score
  
• 303': 100% destruction rate
  
• 305': 100% destruction rate
  
• 306': 100% destruction rate
  
• 307': 100% destruction rate with battleship parts
  
• 308': 100% destruction rate with battleship parts
  
• 310': 30M score
  
• 401': 100% destruction rate
  
• 402': 100% destruction rate
  
• 403': 100% destruction rate
  
• 404': 100% destruction rate
  
• 405': 100% destruction rate
  
• 406': 100% destruction rate
  
• 407': 100% destruction rate
  
• 408': 100% destruction rate
  
• 409': 12M score
  
• 410': No damage nor bombs, 25M score
  
• 501': 100% destruction rate
  
• 502': 100% destruction rate
  
• 503': No damage nor bombs, 15M score
  
• 504': 100% destruction rate
  
• 505': No damage nor bombs
  
• 506': 50M score
  
• 507': 30M score
  
• 510': No damage nor bombs

On close captions there are some notes I had in mind for a few of those.

If what you're looking for isn't listed, I did not record it. Either because it was too early in my playthrough, I thought it would superpose with another mission, or I considered it too easy.

Shoutout to this video for helping on 505 with the destruction of obstables.