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This is the second part of the Hunter and Hunted Mission in Hitman Absolution called the Vixen Club. In this part you enter the Vixen Club and Eliminate Dom Osmond. This guide explains how to complete this mission on the purist difficulty. It does not explain how to complete all the challenges in this area.
When you start go to the right through a door. Immediately to your left is another door way leading to some stairs down. Go down the stairs and into a room which has an air ventilation shaft at the far end. Go through the shaft and the next one once you are out of the first. When you exit that one be sure to sneak because there is a bouncer that will notice you unless you sneak.
Follow the corridor until you get into the Vixen Club. Go around the bar on the far side of the club area and hide in a crowd near the far end of the platform to the left.
A police officer will walk out of the door ahead. Wait for him to have gone past and enter the door he just left. To the left is a bathroom with an employee in it. Go behind him and subdue him.
Hide his body in the cabinet to the left. Be sure to pick up the key card he dropped. Enter the cabinet yourself and wait for Dom Osmond to enter the bathroom (which may take a while).
Be sure to select your fiber wire to get a signature kill on Dom Osmond. Take him out once he is well into the bathroom. Be sure to hide his body in the cabinet too. Leave the bathroom and go back into the main club area. Go towards the back of the club area until you get to a corridor to the right.
Be sure to pick up a bottle from the table at the end of the corridor. Turn around and you will see a door. Go through the door and keep going straight ahead until you are in the next room (not the room with the stairs in it). Either there is an employee in that room or there will be soon.
Go into the cabinet on your side of the room and wait until he is leaving. Then exit the cabinet and take cover on the door you went through to get into this room. Throw the bottle into the corner with the containers ahead.
This will draw away the employee from watching the stairs. Once he is near the door sneak past him and the girl up the stairs. At the top of the stairs you have to pick a lock and once you go through that door it is the end of this part of the mission.