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.
Buy the Shotgun gun.
Buy the Magnum gun.
Buy the TwinShot gun.
Defeat the Horned Boss.
Buy the Plasma Pistol gun.
Unlock the Mime hero.
Unlock the Hippie hero.
Kill a BrainWorm enemy.
Kill a Red Horned enemy.
Kill a Track Shooter enemy.
Kill a Bomber enemy.
Kill a Shredder enemy.
Kill a Hopper enemy.
Defeat the Turtle Boss.
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.
Unlock the Hobo hero.
Buy the SMG 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.