This trophy is titled "Ruler of Kagutsuchi" and it's for playing against every character in online versus play. This would be a royal pain against randoms, so it's strongly suggested you find a partner to play with in either ranked or player matches when going for this trophy.
Each player can start at the character of their choosing, it's suggested you go character by character through the wheel in order to make sure nobody is skipped. The trophy should pop on the final character, so if it hasn't unlocked somebody was skipped.