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