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