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