Here is the full list of all 27 Squareboy vs Bullies: Arena Edition trophies - there are 10 bronze, 9 silver, 7 gold and 1 platinum.
DEFEAT ALL THE BULLIES
THROW A CRATE ON THE NINJA BULLY ON THE SHIP DECK
THROW AN ENEMY
HIT AN ENEMY WITH A SPIN KICK
HIT AN ENEMY WITH A SPIN PUNCH
FINISH THE GAME
DEFEAT BIG BOSS BULLY
DEFEAT NINJA BULLY ON THE SHIP DECK
DEFEAT 300 BULLIES
HIT ENEMIES BEHIND AND IN FRONT OF YOU WITH A SINGLE SWING OF A WEAPON
HIT AN ENEMY WITH A CRATE
HIT AN ENEMY WITH A BASEBALL BAT
DEFEAT BANDANA BULLY ON THE HIDEOUT ROOFTOP
HIT AN ENEMY WITH A CHAIN
HIT AN ENEMY WITH A TRASH CAN
DEFEAT 100 BULLIES
HIT AN ENEMY WITH A BOX
HIT AN ENEMY WITH A TIRE
HIT AN ENEMY WITH A BACK PUNCH
HIT AN ENEMY WITH A JUMP PUNCH
DEFEAT 10 BULLIES
GRAB AN ENEMY
HIT AN ENEMY WITH A STRIKE COMBO
DESTROY ALL THE DUMMIES IN THE DOJO
HIT AN ENEMY WITH A JUMP KICK
HIT AN ENEMY WITH A DASH ATTACK
OPEN THE MOVES LIST IN THE PAUSED MENU