I just tried replaying Allegro Presto and Space Mama's Crater. It's been a few years since I played those, I think.
Allegro Presto reruns (with all the powers) took me about 3 tries to figure out, after which I could consistently beat it without dying. Level 3 is indeed the tricky one, but helicopter helps a lot here. I bet I could make it even easier (skipping a lot of the traps) with running, but didn't need it.
Space Mama's Crater took me 20 lives to beat. I must confess I was quite careless, and with practice I could probably do it without losing more than 5. The trick with the washing machine (on the PC version at least) is to jump over when she fires low, punch the machine. She always fires low (and not high) immediately after that, so jump again, and repeat. After learning all her patterns, it is perfectly possible to avoid even a single hit from her. You need to get a bit lucky and not miss any shots in her initial attack, when she approaches you.