When you talk to Udom on the Groundbreaker. Atempt to turn in Welles.
He'll direct you to Byzantium to talk to Sophia.
Agree to help and the quest "The Demolished woman" starts.
Go to her office abd steal her research first off.
The receptionist sends you over to the bar across the road for her location. If you fail the persuasion check, you can pick pocket the bartender and make your way to the sewers.
On a new playthrough I discovered that you can skip the above and pick pocket the receptionist and let yourself in to her office upstairs (using the lift). Then her location is revealed on her terminal. Next to the Terminal is the research Sophia wants, which will be most helpful.
Find Rachel and kill her for the trophy and Sophias approval.
ExtremePhobia pointed out that this trophy also unlocks if you let the good Doctor live and just turn in the research.
"Just wanted to pass along that you can also choose to let her live and get this trophy. You can retain favor with Sophia by stealing the papers from Rachel's office and turning them in."