Load up the very first level in the first Doom (E1M1: Hangar). Go into the left room and look behind the right pillar for a red button. Press it and quickly run back to where you started the level; to the right of where you started, the wall will drop down and lead to the outside area. You will need to do this quickly or the wall will go back up (if you don't make it just press the button and try again).
Once outside, go into the right room. Go down the stairs and up the stairs at the end. Press
on the wall in front of you to open a hidden door. You will find a secret area and get the achievement.