First off let me say that I thoroughly was enjoying myself with this game and the simple presentation is really fantastic. The art alone probably wouldn't work but the music cements the aesthetic and it works really well.
I think that your game could benefit a lot from coyote time. It's very easy to walk juuust too far off the edge and miss a jump which is frustrating.
I think that while the mechanics here are actually pretty cute and fun, the TAB button is just the wrong button. It is really, really the wrong button. It's super out of the way. Something that my hands are more used to reaching for on games with an arrow keys and spacebar control scheme would be more fitting.
You should probably ditch the platforms during the later phase of the boss fight. They really distracted me and made me think I was supposed to be using them, when in reality by far the best strat for the boss is to just strafe around the bottom of the screen shooting charged shots.
At first I was confused by checkpoints, I assumed they were save points, but in reality if you say, die after getting a new powerup, you still have it when you respawn, and your progress on breaking the walls during the boss fight are kept between attempts to which personally puts me off a lot.
Final comment, there should be a more gradual animation for the charge jump and charge shot. I was under the impression for the whole thing that the big guy can't jump at all until he's fully charged, and it's not super intuitive that different charge times fire the bombs different distances. A bar that shows how charged you are would be really nice.
Overall though this game is super cute and enjoyable and I'm excited to see how you expand on it further.