Here is the full list of all 36 Random Heroes: Gold Edition achievements.
Defeat the Horned Boss.
Buy the Shotgun gun.
Buy the Plasma Pistol gun.
Unlock the Punk hero.
Unlock the Princess heroine.
Unlock the Pirate hero.
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.
Unlock the Ninja hero.
Unlock the Mime hero.
Buy the SMG gun.
Unlock the Hippie hero.
Kill a BrainWorm enemy.
Unlock the General hero.
Kill a Zombie Turtle enemy.
Kill a Worm enemy.
Defeat the Muscled Boss.
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.