I was unable to complete the game as both times I tried it said I still had enemies left but couldn't find any.
I'm not exactly sure how you're handling the double jump currently, but I feel you should have it so the player can double jump at anytime they're in the air/not on the ground (and then prevent them from double jumping again until they touch the ground again).
You could also consider changing the menu slightly. The fact that it's still the default style makes it look very basic and I feel even just changing it to match the color scheme of the game would greatly improve it.
I also felt like the music you used didn't match up with the game, though I did think it sounded pretty good.
It's a good start, and hopefully you can improve upon it in the future.