What a great mechanic. The double jump reminded me of Soldat which I loved as a teenager. There you could only double jump (with a backflip) when running backwards, so it's similar to propelling yourself with the shotgun in your game.
The game is fun but also gets challenging very quickly. I'd love to have some checkpoints to continue from. Otherwise, when you fall badly you risk having to start from the very beginning.
Audio-wise, great acapella. However, I'd love to experience a proper shotgun sound for extra immersion. You could have different sounds for each barrel and when shooting both barrels at the same time.
Fantastic entry!