Very easy to get, Once you've done the speech challenges to entice Elijah to come down to the vault, make a save so that you can come back and get the "Cash Out" achievement.
You need to open the vault door and go left up the small steps to ths area you came in through, you can wait if you want to see Elijah turn off the force field and then come through the doors into the area infront of the vault, but you dont have to.. Now just run back through the areas with the hologram security bots, Dont worry about them seeing you, just keep running through the maintenance shaft until you come back to the lift,
As in the video, just jump down from the level near the alarm terminal to save time..
The achievement should pop before you get to the lift.
If the Youtube video doesn't work, I also uploaded the video here: http://game-play.tv/video/Y9KURD246DDY/Fallout-New-Vegas-Dea...