Cash Out achievement in Fallout: New Vegas

Both Cash Out & Safety Deposit Box can be obtained in one playthrough of dead money.

First save your game before you enter the vault!

Once inside the vault the door will seal shut. Dont worry, just use the terminal at the far end of the room. (note: the 2 at either side of the door disable security systems and whatnot...not important) 

Select the Vera file. (Vera Keyes does nothing that I know of) 
After reading it back out. DO NOT select the new file that appears. Once you back out Elijah appears on the monitor. You need to convince him to come down to the vault. This requires a Lev. 75 barter, repair, or science. Once you convince him to come down this is where you decide which achievement you want.

For Cash Out, wait just inside the vault door gun cocked, dont open the door until Elijah is in the area just outside the vault. (This may take a few tries to judge where he is on your compass) Once he's there open the door and kill him. Achievement popped after he died for me but I've heard rumors of it popping once the fight begins or when he enters the area.

Once he's dead escape, enjoy the ending, and reload your game when your ready.

For Safety Deposit Box, as soon as Elijah says he's on his way down and you can move, run out of the vault, go straight ahead up the stairs, and in the door on your left to the place where you entered this area. Run back the way you came through the maintenance tunnel and when you near the exit maintenance door Elijah will begin speaking. Wait a few seconds and the door will open. Run to the elevator and the achievement should pop once you get on.