Safety Deposit Box

Safety Deposit Box is an achievement/trophy and challenge in the Fallout: New Vegas add-on Dead Money.

Walkthrough
To trap Father Elijah in the Sierra Madre vault, the Courier must have at least one of the following skills at 75: Explosives, Science, Repair, Lockpick, Barter, or Sneak. If necessary, use a magazine before accessing the vault's control terminal.

After activating the Vault Control terminal, Father Elijah will contact the Courier on the green screen behind the terminal. Select any of the following dialogue options when they are available:
 * "Now that I'm here, are you coming down?" Followed by: "Unless you come down here, I'll destroy the vault, everything in it." And pass an Explosives, Science or Repair skill check.
 * "Then I'll find a way to unlock the secrets of this vault, take them for myself." And pass a Lockpick or Sneak skill check.

One can also make a 75 Speech or Barter skill check by selecting the option; "I don't care about the vault, I just want to leave."

After a successful skill check, Elijah will tell the Courier that he's coming down. Two new objectives will appear on your Pip-Boy:
 * Defeat Elijah.
 * (Optional) Sneak out of the Vault's chamber area undetected, trapping Elijah when he opens the vault.

If objective (b) does not appear, reload and try again, otherwise, the blue barriers will prevent one from sneaking out.

Once the player character regains control, there are basically two ways to the exit. One way is to immediately leave the Vault terminal room (make sure to shut the door) and exit the turret room to your left (opposite where Father Elijah enters). Then go through the doorway to ones left and backtrack through the level until you get to the elevator that you arrived in, be careful to not be spotted by Father Elijah. If you are spotted he will activate the alarm and you must kill him. Around the time you get close to the elevator, Elijah will realize that he's been tricked, and set off the alarm.

Another way is to take the short way to the elevator. Immediately after exiting the vault, leave the vault door ajar and sneak to the far right of the door area, into shadow. Elijah will walk down and, with high enough sneak skill, will not notice you. Once he is behind the vault door, he can not see you and you can sneak out. He does eventually see you, but you should be through before he can stop you.

Take the elevator and you will arrive back at the Villa. Your achievement will pop up during the loading screen.