Here is the full list of all 36 Random Heroes: Gold Edition achievements.
Buy the SMG gun.
Buy the Shotgun gun.
Defeat the Horned Boss.
Kill a Hopper enemy.
Kill a Shredder enemy.
Kill a Bomber enemy.
Kill a Track Shooter enemy.
Kill a Red Horned enemy.
Buy the Magnum gun.
Buy the TwinShot gun.
Defeat the Turtle Boss.
Unlock the Punk hero.
Unlock the Princess heroine.
Unlock the Pirate hero.
Unlock the Ninja hero.
Kill a BrainWorm enemy.
Unlock the Mime hero.
Kill a Zombie Turtle enemy.
Kill a Worm enemy.
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.
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.