I switched my fire button to Shift and my jump button to Z. That way, I could alternate between my index and middle finger pressing the Shift key to fire really quickly using either hand. It worked so well I used that configuration for the rest of the game.
On Mother Brain, it mainly just takes a lot of work. Once you've taken out the Zebetites, you should be able to fall into a pattern of dodging and shooting. Just watch out for the turret.