Once you gain access to the Gathering Area, you can enter the deck of a ship (that's stuck on the peak of the Astera base).
At the counter, there is a woman who offers arena quests that would pit you against a monster in an (you guessed it) arena setting.
Choose one, conquer the monster(s) and get this trophy at the rewards summary screen.
Congrats!
Do note that you won't be using your own gear. Each arena quest requires you to don one set of the quest's selection of gear. So be prepared to use gear you might not have used before or at least not as familiar/comfortable with.