Pretty neat look and good old platformer gameplay. I would limit the amount of precision jumps as others have mentioned or I'd use some platformer techniques that allows for snappy platforming so that you don't fall so easily. The background story is good addition and motivation. Overall well designed level for such a short time, good job!
Edit: I see you really get a bunch of comments for platforming. You can check platformer controller that I used in my "Orange square" Trijam game. It's by tarodev, it might solve some of the issues mentioned in comments and be a good aid in the future games.