Nice job on the game. Gameplay is interesting and you created a lot of levels. There's a big delay on the jump causing it to feel extremely unresponsive and gravity feels a little low. The attack animation is very long and also feels unresponsive for a character that feels like they should be a lot more quick and nimble. I love the visual effect when you die. That was a "woah" moment for me.
I had an issue with the first required use of the double jump. When you're on a wall, your jump height is shortened, and I thought the game had wall-jumping rather than double jumping. This particular jump was shortened enough to prevent me from making that jump. So I had actually given up on your game until I seen a comment that mentioned double jumping. To prevent confusion, it might be better to make the first double jump requirement longer horizontally rather than vertically. Many people will assume wall jump over double jump if the platform is a lot higher than further away.