To unlock this trophy, you must complete any of the arena type areas, and complete all 5 rounds. The easiest of these would be the Bandit Slaughter, found in Fink's Slaughterhouse, opposite the fast-travel station in The Fridge.
It is possible to do this on any playthrough, and if you have trouble early on, you can always return to Normal once you're in True Vault Hunter Mode, for example.
Here are some videos of me completing all 5 rounds using my Siren, Magda.