I would sit in the lower right corner at the start and I destroyed the right hand. Then I dodged all of his attacks which is easy to do except for the ones that come from the eyes. Those are a bit trickier since you have to do circular or figure 8 type moves. After doing that, he'll attack with the remaining hand which is flying through the air. If you don't defeat the hand, then he goes back to different attacks (bullet storm, green 90deg bullets, or the heat seeker type bullets) and then back to the hand.
So my strategy was to keep dodging the attacks and keep trying to hit the remaining hand until I was successful. I think I used shark (blue) in the beginning to destroy the right hand and then was using the bombs (black). Eventually I was able to destroy the other hand. It is hard to hit it when it's moving around.