I think even with double jump the jump height is pretty low. Also the gravity feels a bit hard to me. There are platforms which you can't reach. I like the concept idea behind it and the enemies that are hunting you. Right now they can complety block your movement, but I guess thats only a problem because the damage implementation isn't finished^^. I also felt quite lost in the map. Maybe a minimap or some indicators in the level could help to lead the player.
The menu intro transition and music build a great atmosphere!
Overall I think thats a pretty solid game you did :)