The Rematch quests do not count toward the achievement. They are repeatable so you can farm torgue tokens.
Actually, i think they do count, at least for the first time. I had to do the Rematch once to get it off my quest screen. So I think to actually "finish" each arena you need to the three tiers AND the rematch one once.
Currently Playing: Borderlands 2 : Maya Lvl 50 It's not until you lose everything that you are free to do anything