Yep, it can be done. I was missing one of the game mechanics.
This was genuinely fun. Thanks for submitting it!
This is a great entry. Love the theme, the level design, everything. It's so interesting to go back and find that you have to solve parts of the levels differently because you have different abilities.
But I have to ask… are we sure that the last level can be solved on "health" mode? I feel like I've put too much time into it already, but it's the last one I haven't solved.