This is the fourth part of the Hunter and Hunted Mission in Hitman Absolution which is called the Derelict Building. In it you evade the police and make your way through an old apartment building to eventually escape the area unseen. This guide explains how to complete this area on the hardest, purist, difficulty. It does not explain how to complete all the challenges in this area.
At the end of this guide is a visual version of this guide.
At the start of the mission pause for a second or so, then go to a crouch and follow the doorway and through a hole in the wall. Take cover behind a small section of wall in the room you get into:
Wait for the police officer to walk past and then go through the door he just came through. Follow the corridor until you get to the intersection of another corridor which has a police officer standing at the far end:
Wait for the police officer to walk away then go down the corridor and through the hole in the wall up the stairs. You have to jump onto the ledge at the end of the stairs (where they are broken) and ten climb up and edge your way to the platform. Go through the door and to the left until you find a dead body. Dump the body to the lower floor and then make your way through the adjacent bathroom until you get to the edge of a hole in the floor:
Wait for the police officer just visible in the top left corner of the image above to have gone out of sight. Then drop down and make your way towards the cabinet at the end of the corridor to the right. Enter the cabinet and wait until the police officer has walked past the cabinet (which will take some time):
Once he leaves turn around and walk up the stairs. At the top of the first set go to the back right part of the platform and jump up to the ledge and pull yourself up. Shuffle along to the left and the exit is right in front of you. Once you leave through that door it is the end of this part of the mission.