Very good game. On theme, with authentic GB art and direct gameplay actions.
I've got stuck exploring for the first time (maybe the rocks were just a bit out of the frame so I couldn't see the way forward or back), but I've tried again. Didn't get too many treasures since after some I felt the task would be a bit too repetitive, but I've really enjoyed the game in general.
As for feedback, I get that you wanted the museum to be big, but it's too much. With only 4 items there I had to spend minutes trying to find them. This mixed with a very repetitive music was a bit annoying. The world music though didn't feel repetitive, it sounded pretty good. The hook is a great mechanic and makes a lot of room for level design (risky in some cases since it might be annoying to use the hook and be slightly over the water tiles to be sent back).
I think the annoyances of big map or having to repeat a hook are part of the gameboy feel though, so not really a problem.
Good job!