Mission 3: House of Pleasure
For this achievement you will need to first get the Golden Cat Master Key by pickpocketing the Madam, who is in her office (should be labeled on the screen) if you're going the silent route for the game and need to exit the building to meet with Slackjaw, save at her office. From there, head to the steam baths, eliminate or avoid the guards and use the key on the gate into the room with the broken steam pipe. Grab the valve from the nearby table and use it to eliminate your target for the achievement. If you're going kill-free for the other achievements, reload your save at the madam's office.