Ah, I just won. Pretty sure the trick is indeed to not die while collecting powerups, and then not die while fighting the boss; I didn't lose any lives. I had

Ah, I just won. Pretty sure the trick is indeed to not die while collecting powerups, and then not die while fighting the boss; I didn't lose any lives. I had to use all three bombs on the boss, there seem to be three places where there's no way to avoid a hit without the bomb.