Once inside the Casino you will have to track down your three team members once more. You are forced to first turn the power back on in the Casino; do this immediately as with the power on the gambling tables open up for easy chip income. After turning the power back on you must then track down dog in the restaurant. Once inside, you can either convince dog to kill himself (Speech 45) or cure his schizophrenia by... talking to him (Speech 85). You have roughly 15 seconds before dog blows the room up, so talk to him before scavenging for supplies! Also, you cannot fire a shot in the room due to the gas leak; doing so will cause instant death. For a full, detailed walkthrough, check here.
Dean Domino is next on your list, and he's trapped in the Theater. When you are ready, pick up the sheet music in front of the stage; this will initiate a 'race' of sorts from security. Exhaust all options with Dean to know where to run (first his dressing room for Vera's key, then Vera's room for her recording and key). Recording in hand, make your way to the back of the room up to the projector booth and start the holographic show. Then you'll be free to deal with Dean as you wish For a full, detailed walkthrough, check here.
Christine in the most straightforward of the three. She's in the suites in Vera's old room, so simply make your way past the security and radios. Once there, if you haven't already gotten the password from the receptionist's computer you must go back to the main lobby and do so. Bring the password back to her and you may enter the vault For a full, detailed walkthrough, check here.
Make your way through the Vault past security and annoying radios until you make it to the Vault proper. Loot the room before accessing the terminal on the back wall. Once you are ready, convince Elijah to come down and prepare for a fight. Save!
For this achievement, exit the vault bunker once Elijah says he is coming down. He'll emerge to your right (after activating the turret system) and all you must do is kill him. Once dead, the achievement should pop up For a full, detailed walkthrough, check here.