I have this weird strategy of shooting to the left repeatedly in an attempt to glitch the game. Apparently, if you time it just right, when you turn to start shooting to the right, there will be pretty much no limit to the amount of bullets you can pour onto the screen, as long as you don't ever stop shooting (this will hurt your hand). You just flood the screen nonstop and avoid his fire, and when he drops the marble or whatever it is, you can usually get about 10-12 shots off (just make sure you're close enough because the bullets are still subject to range restrictions). If you're good you can wait for him to hover over the ball again and give him the last couple, but preferably you just stop and give your hand a rest, then give him the last bit on the next go using the normal 4 max.
I'm not sure how I get this to work, and it's definitely sporadic (I just use the idle time during the 2nd form to try to get it started). Maybe someone more intimate with the way the game is programmed might be able to explain it better than I can.