Story related, cannot be missed.
This is the first real challenging area that you will come to in the game. Bring lots of health, ammo and parts because all of these are scarce inside. The entire place is overrun with mutants and a few mini bosses along the way (plus an end boss). Also I would recommend at least having 1 if not 2 armor upgrades purchased for this.
You will gain this quest from Dr. Kvasir. He tasks you with heading to the Dead City and picking up an upgrade to your defibrillator unit. Once inside you must wander through the ruins and survive until you make it to the hospital. Finally at the hospital, you must fight off everything and on the second floor all you need to do is pick up the upgrade for the achievement.