Safety Deposit Box

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

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

After activating the Vault Control terminal, Father Elijah will contact you on the green screen behind the terminal. Select any of the following dialog 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.

You can also make a 75 speech 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 you 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 you from sneaking out.

Immediately leave the Vault terminal room and exit the turret room to your left (opposite where Father Elijah enters). Backtrack all the way to the elevator that you arrived in, being 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.

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