All the items that were in this area during the previous section have now disappeared, so there's no point hanging around. Head through the remains of the doorway that Kirk opened for you, and into the small hut ahead. Break the barrel here and pick up the contents, then go back out and follow the path around the building up to the right. On the other side, you can jump down the hole to find another barrel, or go straight through the door ahead with a partner action.
Back Streets
Head through the house directly in front of you, picking up any ammo you find before going out the other side. Get close to the broken ladder and you'll get a very short cutscene; use a Partner Action to give Sheva a boost up and she'll spot a key inside that building - but there's no way in from here.
Follow the alley around, taking out any majini that you encounter, and you'll find another broken ladder just in front of a wire fence. Boost Sheva up again, and she can run back along the roof into the previously inaccessible building to grab the Old Building Key. Some more Majini will show up once she's picked it up; Chris can offer support from the ground while Sheva attacks them from the roof.
Once you're together again, go through the outbuilding and through the door on the right. Another majini will come out of a window directly opposite the door - take him down and then search the room he was in for more supplies. Back in the alley, a majini will attempt to climb over a wire fence to get at you - you can shoot him through the fence if you don't want to wait for him to get across.
Further along the alleyway, a majini will jump out from behind some boxes, and another one will be waiting just around the next corner, at the bottom of some stairs. You can't get into the building through the door at the top of the stairs, but there's a door underneath that you can open.
Inside, pick up any ammo you can find, and grab the Antique Clock treasure from the chest on the left-hand side of the balcony.
Back at ground level, go around the partially locked building to a rusty door - use a Partner Action to kick it down and head through to the next area.
In a short cutscene you'll see a woman being dragged off the balcony of the building ahead, but don't go to her rescue just yet. If you picked up the Old Building Key earlier, use it on the small building in the middle of this area to get an Ithaca M37 shotgun. There's also a chicken on top of this building; chase it for a bit and it'll drop an egg, which is useful as a healing item or for getting the Egg Hunt achievement.
When you've searched the area thoroughly enough, head up the steps on the building for another cutscene. As soon as it ends, the woman will attack you - take advantage of your new shotgun and blast her. A parasite will burst out of her head when you've dealt enough damage, but it's just as dangerous. Keep shooting it and it'll eventually die; you'll be able to recover the Ivory Relief treasure from her body.
Grab any other items from this room and the next, then head out the door and down the steps. There are a lot of majini in this area, but you don't have to fight them all - run around the back of the shipping container and you'll find a hole in the wall that leads straight to the door out of this area. Regardless of your preferred method - either running or fighting - use a Partner Action on the door to leave when you're done.
Abandoned Building
Climb the stairs and follow the corridor around. The body of one of the Alpha Team soldiers falls from around a corner, but it's no threat. In the next room, smash the barrels and crates as you make your way up the inside of the structure, then use a Partner Action to open the door into the next room.
You'll get a short cutscene in which DeChamp, the leader of Alpha Team, gives you a hard disk with important intelligence about your target, Irving. Alpha Team has been attacked by an unidentified bio-organic weapon, and it's now left to Chris and Sheva to continue with the mission.
Once you're back in control, grab any supplies you need from this room, then head into the corridor and take the lift down.
Basement Furnace
Follow this narrow corridor along until you come to a large room - the door directly ahead is locked, so you'll have to find a key before you can proceed. Smash the crates and barrels here to stock up some more ammo, then head down the side corridor to find the furnace itself, and the Furnace Key beside the body of one of Alpha Team's former members.
It's worthwhile examining the layout of this room while you've got some time; make a careful note of the location of the doors on the furnace, and where the activation switch is.
Head back to the locked door, but be ready for some pretty heavy opposition.
With the BOW defeated, go back to the locked door and use the Furnace Key to open it. Head along the corridor, stocking up on handgun ammo from the attaché case, then get into and use the elevator to end the chapter.