Ok, I came into this game knowing it would be difficult, but there are some serious balancing issues here that need to be addressed.
The first two rounds are beatable, even before I figured out that I had a double jump. The big issue is with the boss battle.
First of all, the collision box of the boss is too tall. I was getting hit by him even when standing on a platform clearly above him.
Second, when the enemies start coming in during the boss battle, it's impossible to fight them because, as soon as you divert your attention, the boss jumps over to you and doesn't let you fight them, forcing you to divert your attention back to the boss.
Third, the boss has way too much health, in my opinion, and having a display that shows it would be extremely helpful for players to track their progress.
A good game design point I like to follow is that the perceived difficulty of the game shouldn't increase unexpectedly; it should match the skill of the player. Right now, the shift to the boss is a very high skill spike.
Hopefully this advice helps. Other than that, the art style is great, and the player movement/attacks are very satisfying. Good job!