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.
Buy the TwinShot gun.
Buy the Magnum gun.
Defeat the Turtle Boss.
Unlock the Punk hero.
Unlock the Princess heroine.
Unlock the Pirate hero.
Unlock the Ninja hero.
Unlock the Mime hero.
Buy the SMG gun.
Kill a BrainWorm enemy.
Unlock the Hippie hero.
Kill a Zombie Turtle enemy.
Kill a Worm enemy.
Buy the Shotgun gun.
Defeat the Muscled Boss.
Unlock the General hero.
Unlock the Dino hero.
Unlock the Professor hero.
Unlock the Hobo hero.
Unlock the Agent hero.
Find a Crystal Skull.
Unlock the Trucker hero.
Kill a Zombie Runner enemy.
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.