The theme interpretations are very literal, nice choice on the edge getting cut so you become more "on the edge" as the "boss" intensifies. I'll admit its hard, I kept dying at the 32-33 hp mark, difficulty ramps up significantly once the third stage hits.
Art wise, paper/doodle graphics are always a fun take on things, good execution on it and especially the boss design. Music is good but a little repetitive.
The "worst" thing is, there are all these cool power moves like speedy dives and quadruple jumps, yet none of it seems to be of any use in the actual combat against the boss. It doesn't seem intuitive how these abilities can be applied vs the boss, when the edge/ledge is so small in the end.
This just means your idea has potential and a fuller implementation could bring a lot of fun to a paper platformer with this boss guy at the end. Good job!