Youtube videos of platformers make them look ridiculously easy.
Anyway, I always thought that to get the extra height you had to press and release A exactly as you hit an enemy, and that there was a very narrow (almost frame-exact) timing window. Except that's almost completely wrong. In reality, you have to be merely holding A as you hit an enemy, the window for when you can start holding the button is frankly massive (up to maybe half a second in advance?), and it doesn't matter at all when you release A. That discovery made that bonus level quite a bit easier... well, it still took me about half an hour of extra attempts to finally reach the end, but at least I could now get past the fourth set of barrel cannons about 30 seconds in.