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