Yeah, I've beaten the game already. But I know that all the missions have to completed in the same "mode" for the achievement to pop, which is why I haven't upgraded to TVHM yet. I'm level 32; is this high enough to farm Warrior a couple times solo?
You can go to TVHM and play and go back to normal mode at any time. You won't be able to beat all the missions (see You.Will.Die.(seriously)) until level 50 at least, and leveling to 50 in normal mode will take forever.