I really like it.
If I could make some suggestions though:
Don't take the player back to the start screen on death and make them go back to their keyboard and hit start. Just immediately spawn them back at the spawn point. One of the biggest pains in a game where you repeatedly die over and over again is counting up the amount of time you spend waiting to get back into the level. With a game like this, before you get a clear on the hardest levels, you'll spend a huge amount of time just waiting for screens to change. Many people will quit not because they don't want to play the level but because they don't want to wait to try again anymore. It seems like its not a big deal but when you die frequently it is.
IMO, the player moves too far left/right from a very slight input. It would feel better if you could move very slightly with a small touch.
Also, let the player use D-pad for movement on controller in addition to analog. It allows more precision.
Also, in some of the harder levels, its ambiguous whether its the top or bottom character that is dying, which makes it hard to figure out what you're doing wrong. There should be some kind of clear indicator which side caused you to die.
Good job.