Just a note: I missed the first two secret levels, so you can skip the secret levels and still get this achievement.
Like One Eyed Tigh said, save often. Remember to use the chainsaw on Demons and Spectres because they don't shoot any projectiles. Stick with the shotgun most of the time but use bigger weapons on the bigger enemies.
If you get stuck check the Doom wiki for maps and secret room locations.http://doom.wikia.com/wiki/Category:Ultimate_Doom_levels