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