I went into this game with pretty low expectations, but it actually turned out to be a surprisingly decent platformer! There was a lot of good variety in the enemy, level, and environment design, and the bosses were all pretty neat, too!

That said, there were some glaring flaws that were tough to overlook.
1) Checkpoints felt needlessly unforgiving. The early levels in this game are pretty short and easy, but later in the game things do get challenging, and I'd appreciate a bit more margin for error. I ended up quitting on Purgatory because it felt like I was losing too much progress on each death, and I just didn't want to repeat such large chunks of a level over and over.
2) The camera is too focused on the player character. I found that there were actually quite a few jumps in the game where Faust would go so far above the next platform that it failed to be visible on screen. I'm surprised that I never actually died as a result of this, but it's still very unpleasant. One useful trick I've seen to try and fix this is to have the camera scroll up and down to match the player's Y value only when they're actually standing on a platform. If they're in the air, the camera will only track their X position.
3) The borrowed music assets really felt kind of cheap and lazy. For a small project like this, you can pretty much get away with taking songs from other sources without worrying about legal action, but you have to be careful about what songs you take. If you just grab a boss melody from Undertale and drop it into your own game, your game looks like a bit of a copycat and suffers for it (I also noticed tunes taken from Transistor and Crypt of the Necrodancer). It's usually best to try and grab songs that aren't super well-known from other sources, as it will help your game to have an identity of its own. You can look on Newgrounds for all kinds of music that artists would love to give you for use in your game, and Incompetech.com for a ridiculously large collection of totally free music to use in any project.

I also had two smaller complaints that didn't detract too much from the experience, but would have been nice anyways.
4) Some of the character sprites felt a little crude. I think I felt this the most in the fight against Ignis - when he strikes the ground as part of his leaping attack, he just kind of plops there. It would be cool to see his knees buckle a little or have his sword really get stuck in the ground for a moment. Little stuff like that would really help to sell the game's art and animation a lot more than what you have now.
5) Lastly, I don't think you went far enough with the special effects. You could probably have afforded to put in quite a few more particle effects. And a bit of screen shake when the player gets hit or fires their weapon would really help make the game *feel* a lot better.

At the end of the day, I think this is actually a really cool start, but there is still plenty of room for improvement. Keep working at it! I can't wait to see what you come out with next!