Shoot ALL of the barrels in level 3 and a bridge will appear which you can then cross to get over the acid pit to reach the door. Enter the room and kill ALL the enemies and find the hidden exit and activate it to access the secret level.

On the 'Hurt Me Plenty' or higher difficulty setting get a 100% kill rating on any level.

On Nightmare difficulty setting beat any level to receive a Gamer icon of a Demon.