Here is the full list of all 11 River City Melee: Battle Royal Special trophies - there are 7 bronze, 3 silver and 1 gold.
You have won against Munakata and Matsudo's (boss) teams.
You have played against all teams.
You've engaged in online combat.
You have cleared Story Mode.
You have won without using a special move.
You've damaged your opponents on a bike in Pier Stage.
You've used Body Check (triple combo) in rage as Hasebe of the Cheerleader Team.
You've turned the slot in Factory Stage.
You've scored the ball in Ground Stage.
You've engaged in free battle.
You've destroyed the floor in Fight Destruction Stage.