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