Here is the full list of all 37 Random Heroes: Gold Edition (EU) trophies - there are 22 bronze, 9 silver, 5 gold and 1 platinum.
Get all other trophies
Buy the Plasma Pistol gun.
Defeat the Horned Boss.
Kill a Shredder enemy.
Kill a Bomber enemy.
Kill a Track Shooter enemy.
Kill a Hopper enemy.
Kill a Red Horned enemy.
Buy the Shotgun gun.
Defeat the Turtle Boss.
Unlock the Punk hero.
Unlock the Princess heroine.
Unlock the Pirate hero.
Buy the TwinShot gun.
Unlock the Ninja hero.
Unlock the Mime hero.
Unlock the Hippie hero.
Kill a BrainWorm enemy.
Kill a Zombie Turtle enemy.
Kill a Worm enemy.
Buy the Magnum gun.
Buy the SMG gun.
Defeat the Muscled Boss.
Unlock the General hero.
Unlock the Dino hero.
Unlock the Professor hero.
Unlock the Hobo hero.
Unlock the Agent hero.
Find a Crystal Skull.
Unlock the Trucker hero.
Kill a Zombie Runner enemy.
Unlock the Lunatic hero.
Unlock the Gentleman hero.
Kill a Flyer enemy.
Unlock the Cop hero.
Kill a Zombie Shooter enemy.
Kill a Zombie enemy.