Here, timing should be near perfect.
My strategy is be all the way to the left.
First, jump avoiding the bullets, you will have to jump a little before you should do it, to be able to jump again in the next burst.
Second, you have to avoid the missiles, if you are all the way to the left, you will have to perform two precise jumps for each set of missiles. The idea here is to jump, right after the missile on you left/right passes you. Do this two time.
Third part is the easiest, simply shoot the bubbles and then shoo the boss.
Rinse and repeat. You can see this strategy on the following video:
Sorry, this Game Clip has been removed