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.
Unlock the Mime hero.
Unlock the Hippie hero.
Buy the Shotgun gun.
Defeat the Horned Boss.
Unlock the General hero.
Unlock the Dino hero.
Buy the SMG gun.
Kill a Hopper enemy.
Unlock the Professor hero.
Kill a Shredder enemy.
Kill a Bomber enemy.
Kill a Track Shooter enemy.
Kill a Red Horned enemy.
Defeat the Turtle Boss.
Buy the Plasma Pistol gun.
Unlock the Hobo hero.
Kill a BrainWorm enemy.
Kill a Zombie Turtle enemy.
Kill a Worm enemy.
Defeat the Muscled Boss.
Unlock the Agent hero.
Buy the TwinShot gun.
Unlock the Trucker hero.
Unlock the Lunatic hero.
Find a Crystal Skull.
Kill a Zombie Runner enemy.
Buy the Magnum gun.
Unlock the Gentleman hero.
Kill a Flyer enemy.
Unlock the Cop hero.
Kill a Zombie Shooter enemy.
Kill a Zombie enemy.