At the end of the game you will return to Arizona.
After getting there you will be just outside the Citadel. Talk to Vargas, he will ask to join you on the assault, say yes. There are also other allies scattered around, you can use the map to see them. Just walk to them and they will ask if you want them to help. If yo usay yes they will assist you in assaulting the base (they control themselves.) In order to get this achievement you will need to complete the assault and have none of those allies left EXCEPT Vargas. The obvious choice is to not take any others but the final fight is a huge pain in the ass, especially trying to keep a very weak and stupid Vargas alive, so having other cannon fodder around is helpful. Also, once it is over, all you have to do is go and murder the remaining allies.
Once you have done all that and the only NCP alive is Vargas, head upstairs and talk to the person by the helicopter, you will then have to go find the nuke, which is in the room down the stairs to the left. Select the nuke, use the dialog option that says "The timer is busted" and Vargas will offer himself up. Try to talk him down but he will not and he tells you to get out. Boom, achievement popped.
Also be sure to have the gorilla costume on if you have it for another achievement.