The Outer Worlds The Demolished Woman Quest
Dock at Akande’s personal landing pad and head through the doors ahead. After a brief pause in which you are cleared, go forward to the elevator and take it to the top floor. Talk with the receptionist, Percival, and show him Udom’s badge. He will patch you in via video feed to the Adjutant, who will introduce herself.
To prove you are not working with Phineas she will task you with assassinating one of her cartographers, Rachel Lockwood, which triggers the next story quest: The Demolished Woman.
Take the lift downstairs, leave the building, and enter Byzantium proper. The Bureau of Exploration is straight ahead, so travel down the stairs and across the estates. Round the corner to the right and you’ll find it to your left. Enter the building and you’ll see a Mr. Sherman Bradshaw to your right.
Talk with him, and if you can pass an intelligence check you will recognize him as the other freelancer Akande sent to kill Lockwood. He will inform you that Lockwood hasn’t shown up in hours, and will propose a competition: who finds her and kills her better gets the contract.
Before leaving, ask for access to Lockwood’s office to retrieve the documents Akande requested. Go through the door and up the elevator. Lockwood’s office is down the hall and on the right.
Use the key Bradshaw gave you, grab the documents, then use the terminal to locate Lockwood. Reading her messages will reveal she is on to the plot to the assassination plot, and is taking refuge in the maintenance shafts.
Leave the building and you’ll see the tunnel leading to the shafts directly ahead. Head in, turn right, and take the elevator down. Once inside just follow the quest marker to find The Demolished Woman herself hiding in a corner.
Talk with her, and Bradshaw will show up to discuss how you’d like to dispose of the frightened cartographer. You can split the earnings, listen to what she has to say, claim the kill for yourself, or spare her.
If you hear her out, Lockwood will offer to pay the full bounty to both of you, but Bradshaw has cold feet. A 55 Persuade will change his mind, however, if you are fine with sparing the lady and lying to Akande.
Regardless of how you handle Lockwood, The Demolished Woman will task you with returning to Akande. Leave the maintenance shafts and head back to the HHC building on foot, or via fast travel. Return to Percival at the front desk and report the news. She’ll ask about the choice you made, revealing she was watching you the whole time.
If you earned Akande’s trust she will ask you to place a trace within Dr. Phineas’ communication terminal at his lab. This will unlock the story quest Long Distance, but it resolves a little differently at this junction.