Yeah, veterans of the game know who Max is.
Yes, you can kill him, it just takes a LOOOONG time (unless you cheat or something).
Try running around and reflecting his shots back at him. It takes time and patience, but you can do it! Of course you don't have to kill him...
And you can kill him in the room you find him at if you hit him without "activating" him (that is, don't press space bar, just wail away).
You can also kill Wee Gee...