Like many games, this fight moves through a few phases, alternating between times where you just have to survive, and times when you actually try to attack back.
The first phase involves lots of jets of fire filling his room that you have to avoid. From the top, the sides, etc. It's tricky, but not too bad, really. I've just about got this phase finished. Next will be a part where you can fly up and try to get a shot off with your laser before he starts shooting fire at you again.
|Geez, in this picture, you can't even SEE Dr. Squidbrain because of all the fire.|