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
OPEN THE MOVES LIST IN THE PAUSED MENU
HIT AN ENEMY WITH A STRIKE COMBO
HIT AN ENEMY WITH A JUMP PUNCH
HIT AN ENEMY WITH A JUMP KICK
HIT AN ENEMY WITH A BACK PUNCH
HIT AN ENEMY WITH A DASH ATTACK
HIT AN ENEMY WITH A SPIN PUNCH
HIT AN ENEMY WITH A SPIN KICK
GRAB AN ENEMY
THROW AN ENEMY
HIT AN ENEMY WITH A BASEBALL BAT
HIT AN ENEMY WITH A CHAIN
HIT AN ENEMY WITH A TIRE
HIT AN ENEMY WITH A BOX
HIT AN ENEMY WITH A TRASH CAN
HIT AN ENEMY WITH A CRATE
HIT ENEMIES BEHIND AND IN FRONT OF YOU WITH A SINGLE SWING OF A WEAPON
THROW A CRATE ON THE NINJA BULLY ON THE SHIP DECK
DESTROY ALL THE DUMMIES IN THE DOJO
DEFEAT BANDANA BULLY ON THE HIDEOUT ROOFTOP
DEFEAT NINJA BULLY ON THE SHIP DECK
DEFEAT BIG BOSS BULLY
FINISH THE GAME
DEFEAT 10 BULLIES
DEFEAT 100 BULLIES
DEFEAT 300 BULLIES