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