I really liked the music and the graphics style.
The blind jumps are really frustrating tho! The simple way to get rid of this problem is to make the player travel shorter distances mid-air, so a shorter double jump and a slower movement speed will do the trick. This means that platforms will be closer together and in screen space. Also, whenever the next platform is far away and not visible, assume that the player will perform a 'Leap of Faith'. A 'Leap of Faith' is what I call when players hold a direction button and do a perfect double jump to get the most air time and distance covered possible in hopes that they'll land on to the next platform which is not yet visible. You can also guide the player mid-air using collectibles. For reference you can see in the game Crash Bandicoot: The Huge Adventure for the GBA the developers used wumpa fruits (the game's main collectible) to guide the player through long blind jumps.