The entire game gave me hell, past level 1. As for other picks:
Guts Man's stage from MM1. For some reason, as a kid, I could NEVER get the timing right for the conveyor part at the start. I ultimately flaked out and used the Magnet Beam. However, I could get through Ice Man's 'pop gun' platform sections without using the Magnet Beam.
Quick Man's stage from MM2, without using the Flash Stopper. It was gratifying once you got down the rhythm of going through those beams without getting pegged, but until then...