Wowie! The platforming (albeit a little too quick for me), visuals, and audio are all super polished! And the idea of not only beating the level in a time limit, but coming around to kill yourself is really creative and unique!
Also having the win/lose of your game change the path your character goes on in the levels is a super cool touch. Makes it much more replayable. Big plus! (Quick bug report, when I won twice, lost once, and won once, it took me to the 3 wins, no loses level not to the 3 wins, 1 loss level)
I love how you implemented coyote time and auto-edge vaulting when jumping at a ledge. I don't know if it was just me, but it didn't seem like the auto-vault would happen if I was wall jumping and slid up the wall. I feel it would be cool to add if it's not already there that if your sliding up the wall and reach the corner you do the same thing. A lot of the wall jumping areas felt like you were only a few centimeters away from making it.
Great job! One of my favorites by far :D