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