Right off the bat:
1) The change of UI control isn't nice. You switch from "Press Enter" to get past the intro, to mouse click on the main menu, and then back again in-game. You want these to remain the same for fluidity.
2) The first time I tried playing, I had no idea what I was supposed to do after listening to the tape. I didn't see the tip at the top of the screen. I'd recommend making it apparent by adding a shadow or making it a different color.
3) Who did that voice acting? It was terrible! ;P
4) I think you did the same thing that I did with my first game: You made it harder as you made the game, not realizing you were just getting better at it. You should knock down the timing of the "killers", especially since this is the first boss.
5) The character is a bit sensitive for the movement style. The platforms need to be bigger, the player needs to move slower, or the jump needs to have a little die-off instead of dropping straight down when not pressing on the movement keys. (If you did one of these, it might solve #4)
6) You should give the player an object to challenge. What I mean is create a visual for the enemy, or change the script so that the player has something to fight rather than just rhythm. One way to do this is to put the enemy's sprite in the background, and draw it to look like the enemy is somehow controlling what's happening.