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