Why not play through TVHM and get up to level 50 first at least? Unless you're geared very properly, fighting him at 34 is just way too hard. Plus zer0 has a lot of great skills the higher of a level you are.
@sirkibble: If you're farming for eridium, I think the warrior would be better. Not only is he easier to kill but I'm pretty sure he drops more per kill as well. Yes UVHM is quite a nightmare especially when you first jump into it as you become gear checked almost every 2-3 levels lol.