Okay, GREAT idea here, and some EPIC (if maybe melodramatic, but I suspect that's the Rayman aesthetic) presentation! But you gotta work on some of the visuals and mechanics!! Here are my suggestions, as in what I personally think could be done:
1. For God's sake, why does the cursor, which is already wicked huge and gets in the way of other squares, have to flip (and somewhat randomly since it's tied to velocity)? And not only that, why does it flip the hotspot of the cursor when it does? If you really want it to flip, flip it around the hotspot. I realize that you need something with a hitbox for the boss battles (which is a really novel idea, even if I'm not the biggest fan), but maybe tweak it a bit?
2. Having the P mark the Xed squares makes it kinda tricky to see. I ended up making some mistakes because of it. Perhaps have it cover the whole square? Or maybe just an X?
3. LET US SKIP THE TUTORIAL PLEEEEEEEASE QwQ
4. You have both a time limit AND mistake limit. That's...a bit much. Not only that, but you only get to make two mistakes before the next one ends the whole thing. With the difficulty telling what's what, and the flipping cursor, players could end up slowing way down. It also stresses folks out. Please either leave the health bar for boss battles, increase how much health we get, or both.
5. In addition to the Ps for Xes being odd, please change the font of the numbers to be simpler. When smaller, it's harder to figure out what they're supposed to be. There's nothing wrong with having boring fonts for numbers--legibility is paramount!
6. Something that helps a lot in the actual Picross games by Nintendo is having the numbers marked off as they're filled in for certain. That way, when a row/column is finished via clearing other ones, you know for sure. Some games even automatically fill the remaining gaps with Xes, but I'm personally not a fan of that. It's nice to X boxes out :)
7. Why is there no options menu?
Overall, definitely a lot of passion in this, and full of charm. The boss fights go against normal Picross sit-n-chill (I personally hate time limits and mistake penalties, as it is), but with only two attacks, it's not too hard to dodge. Just remember, you're already asking a player to think really hard for some puzzles--the fewer distractions, the better. I'm not sure I'm sold on the boss fights, honestly.
Do keep working on this, it's certainly a love letter to Rayman. I'm not very familiar with the series, but I'm a big fan of nonograms--that's where all my critique stems from. (Well, okay, there's one bit of critique on the Rayman side...why did you make beta!Rayman(?) look so...offputting? XD; ) This has a LOT of potential, and I wanna see this become a really cool fangame! But it still needs some work, IMO.