Here is the full list of all 36 Random Heroes: Gold Edition achievements.
Unlock the Punk hero.
Unlock the Princess heroine.
Unlock the Pirate hero.
Unlock the Ninja hero.
Defeat the Horned Boss.
Unlock the Mime hero.
Unlock the Hippie hero.
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 General hero.
Kill a BrainWorm enemy.
Unlock the Dino hero.
Kill a Zombie Turtle enemy.
Buy the Plasma Pistol gun.
Buy the TwinShot gun.
Buy the SMG gun.
Unlock the Professor hero.
Unlock the Hobo hero.
Kill a Worm enemy.
Buy the Magnum gun.
Buy the Shotgun gun.
Defeat the Muscled Boss.
Unlock the Agent hero.
Unlock the Trucker hero.
Find a Crystal Skull.
Kill a Zombie Runner enemy.
Unlock the Lunatic hero.
Unlock the Gentleman hero.
Kill a Flyer enemy.
Kill a Zombie Shooter enemy.
Unlock the Cop hero.
Kill a Zombie enemy.