I do wish the cannon wouldn't get blocked by bugs when shooting at ones with secrets. This game may be drawn in 2D, but you're shooting away, not upward, so there's no reason why it can't hit bugs at the top row while there are bugs at the bottom row.
I find it odd that once you've beaten the puzzle, you can play it again for a better time, even though doing so means you can have the solution fresh in your mind and just put it in. Or, if you're particularly unscrupulous, just jot the solution in a notebook and copy it from there. Having medals in this kind of game doesn't work, and it's very easily abused, especially the way you implemented it.
I don't mind the fact that each class has its own level. In fact, it adds a bit of strategy to the game, where you can choose to focus on one job or branch out to several. What I don't like is how changing your class changes your character entirely. HP and SP ought to carry over in a class change, at the very least. It'd be nice to change classes in battle as well.
The level layouts really bad. It's practically impossible to know where you're going, especially when jetpacking around, and there's absolutely no indication of where you're meant to be going. Everything feels disorganized and shoddily designed. And that kills it for me more than the "unusual controls."
Some nitpicks I have in the first few minutes playing:
The music playback is pretty low quality, and the tune used is definitely more fitting for the last few levels.
The instructions section is only two pages long. You can just use one button to flip between both pages.