Actually I think you can hit it with the arm up, too (on my 1:37 run I'm pretty sure I was able to do that) but the head must be up to allow the missles to make it there. He's a pretty easy boss once you get used to him.
Quote from Bladegash:
THe blinking light on its chest is the only place you can damage it. The arm has to be down and the head has to be up to be able to hit it.