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