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