After completing the first mission in the area, you'll unlock various tasks on your map. Find the point "Gilly the Kid" and talk to the Night Cap to start the mission. Complete the quest to unlock the achievement.
*** Spoiler - click to reveal ***
You are looking for the Grizzled Cowboy's Hat. You need to hack the security doors to obtain it.
1) Open the Electrified Door by sabotaging power generators (4).
2) There will be a cutscene in which you have to open another electrified door by sabotaging power generators (again) (5) but this time you have to prevent the zombies from repairing it.
3) When you attempt to pick up the hat, the hat falls into the cheese and the lab gets overfilled with cheese. You must now attempt to escape the place. You have plenty of time to escape with plants who are unable to move fast.
The quest is now over and the achievement should unlock!