To beat arthur:
Get on his side of the screen. He'll naturally move to yours. He'll keep jumping around as you rapidfire at him, and he can't turn in midair, so he'll be facing the wrong way the whole time and won't throw anything your way. And if he does, he usually changes direction again back to the wrong way. Just spam the buster on his side of the screen and you'll quickly murder him!
If necessary, you can go down the ladder and wait for him to come down, then you quickly go back up and he follows and if you shoot him the very instant he's back up, he's facing the wrong way again and you're doing it again.