The collision boxes for the spike things were both too forgiving when you were on top of them and not forgiving enough when you weren't even touching them. I would have played the entire thing, but there's no way to restart at the beginning of the level, you can only reboot the game and start over from the very beginning. There's also no feedback for the gun, and when you use it in the air or on certain platforms you get teleported backwards which really messes with platforming.
If you just add a way to restart at checkpoints and fix the hitboxes, I'm sure you'll have a fun, simple platformer on your hands.