I managed to solve the lava section, but I seem not to get what to do in the other areas (also, the entry to the north area got blocked by the enemy at some point). I fear I get frustrated too fast, so checkpoints could help (maybe there are, and I just failed to get one). However, I like the art style, and everything seems to work, so great work! Maybe I'll come back later and collect some hints from the other comments.
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I made the puzzle not so easy, because thats the game objective :P
But here below some hints, since they arent easy:
For the water enemy, if you stop moving, see its behavior. Then if you move, how can you use the level at your advantage?
The left side is really just exploration, while the right side, I gave some hints how to solve it ;)