Here is the full list of all 36 Random Heroes: Gold Edition achievements.
Buy the Plasma Pistol gun.
Buy the Shotgun gun.
Defeat the Horned Boss.
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.
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.
Defeat the Muscled Boss.
Unlock the Mime hero.
Unlock the Hippie hero.
Buy the SMG gun.
Unlock the General hero.
Unlock the Dino hero.
Unlock the Professor hero.
Unlock the Hobo hero.
Find a Crystal Skull.
Unlock the Agent hero.
Kill a Zombie Runner enemy.
Unlock the Trucker hero.
Buy the Magnum gun.
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.