This was fun! It reminds me of playing cat Mario back in the day, trying to remember all the traps in the level. Really tough so I only got to level 2, but that seems fitting with the style of game. Player handles really well, especially the double jump. Love the players little flip when they double jump and some of the animations are really nice.
Some feedback when the player takes damage could help a lot, maybe a sound effect and bit of screen shake as there were a few times when I was trying to dodge enemies shooting at me where I wasn't really sure if they'd actually hit me or not without checking the health bar. Don't think the tutorial mentioned that you need to collect all of the cherries to complete a level so I initially thought it was a bug when I reached the flag at the end of level 1 and nothing happened. Might be worth adding this info to the game page.
Overall good entry! Nice job.