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 Shotgun gun.
Defeat the Horned Boss.
Buy the Plasma Pistol gun.
Kill a Shredder enemy.
Kill a Bomber enemy.
Kill a Track Shooter enemy.
Kill a Hopper enemy.
Kill a Red Horned enemy.
Defeat the Turtle Boss.
Unlock the Punk hero.
Unlock the Princess heroine.
Unlock the Pirate hero.
Buy the SMG gun.
Unlock the Ninja hero.
Unlock the Mime hero.
Kill a BrainWorm enemy.
Unlock the Hippie hero.
Kill a Zombie Turtle enemy.
Kill a Worm enemy.
Defeat the Muscled Boss.
Unlock the General hero.
Unlock the Dino hero.
Unlock the Professor hero.
Buy the TwinShot gun.
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.
Buy the Magnum gun.
Kill a Flyer enemy.
Unlock the Gentleman hero.
Kill a Zombie Shooter enemy.
Unlock the Cop hero.
Kill a Zombie enemy.