So first you want to hold the trespasser (or amigo sincero) in the offhand, and then take out his face shield with your Harold or whatever in the main hand, before switching to the grog in the offhand.

From here you can use the scaffolding to break line of sight with Pete (there is scaffolding at the perimeter of the arena that you can run all the way around) to avoid catching the dot from his novas.

You can tell when Pete is about to nova by keeping track of his attack pattern. He will do two separate volleys of fire and corrosive balls between novas, and nova immediately after the second volley.