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