Note: There are neither collectibles nor optional dialogue in this chapter, so you can just 'sit back' and enjoy the ride as you play through it.
Head up the stairs and leap to the building up ahead. A guard up above a balcony will become suspicious, just to learn you the game mechanics of stealth. The white threat meter will fill when there's a chance of you being spotted. It will turn yellow when they're going to investigate the suspicious movements. Stay out of their sights and they'll go back to their normal behavior after a short while.
Keep hanging from the ledge to make it around the building (move to the left side). Keep hanging from the roofs here to avoid being seen. Climb the building and throw the guard down, then go inside. Drop down the other side, on the rooftops below, but watch out for any flashlights. Quickly move to the nearby building to the left and keep continuing to the left, using the pole here to swing to the building up ahead. Move through the hall and make your way to the small balcony at the end. Here, jump to the lower roof to the right. Be careful going around the corner, because there's a guard with flashlight searching these roofs. When the coast is clear, quickly make your way across (a little to the left) and climb up.
Continue left to make it to a small square with some tall grass. Although you can hide here, it's better to just quickly head to the (far) right side of the square and climb the pillar here. You'll avoid the guard entirely this way.
Climb the stairs and make your way to the small roof at the left of the building. From here you can climb the building. Once on top, climb the smaller roof to reach an open window. Try to open the doors and Nadine will cross your path. A fight ensues. You can't beat her, so just do your best to get in a few punches. After the scene, use the poles to reach the building up ahead and climb to the right to reach a small roof. Leap to the small hexagonal rooftop on the other side and cross the balcony terrace.
Now's a good time to check your surroundings. You should be able to spot a round sign just behind a round balcony somewhere; that's the direction you need to go. From that small round balcony, leap to the pole and swing towards the building to reach the round sign. It turns out to be too weak to fully hold Nate's weight, so you'll attract some guards. Sam throws you a gun, so take out the two guards with it.
Make your way to their bodies and loot the ammo they were carrying. More guards soon appear. When you're still unseen - in stealth - you can mark enemies by holding L2 and pressing L3 (the left stick). Continue by leaping to the balcony/walkway on the right, when the guard is looking away. Punch him from behind when you get the chance., preferably inside.
The next guard is up ahead on the walkway with long grass. You should be able to jump to the window and quickly climb up to his position. He will be alarmed, but you can pull him down anyway. Be careful as you continue, because another guard is coming up the stairs. Hide behind something (or in the grass) and knock him out cold from behind. In any case, if you're spotted, simply take out the upcoming guards in a firefight.
Head into the building downstairs and proceed towards the next, where various guards are patrolling. Defeat them in a firefight. Drop down a roof and look further down; there's another roof below. Jump to it to reach a square with tall grass. At the opposite side you can find a wooden boxcart; push it to the canopy in the middle of the square. Some guards will appear; take them out any way you like, then climb the canopy to reach the balcony and adjacent roof, where you'll find a long rope that you can slide down.
You come crashing Sam's firefight party. Quickly start taking out guards closest to you, especially the ones with shotguns. Hide behind pillars and clear the place out, then make your way outside. Defeat more guards on the stairs and finish the last part of the firefight in the pool with statues down below. Hop in the car when the coast is clear to finish the chapter.