When you kill the first three gorillas, climb up onto the balcony above (as shown in the first screenshot to the left). When you pull the switch, jump down either to the floor, or into the water, and then make your way through the door.

When you reach this movable box, pull it out just a little. Then, immediately climb onto it and roll through the opening ahead and into the small room with the switch.

Once you pull the lever on the balcony of the room with pillars and spikes, wait a few moments, and then run slightly to the left and jump to either grab or land on the pillar with spikes. Immediately jump onto the slope to the left before the spikes come out. This will save you some time, but note that you can easily get hurt and/or knocked down by doing this.

When you exit the room with pillars and spikes, go left and use the cracks to the left side of the Midas statue to make your way up (first screenshot to the left). Then pull the switch and carefully make your way down by rolling over the edges (be careful not to step on Midas' golden hand). Turn left and go through the door (as shown in the second screenshot).

When you have to wall-run at this point, keep holding forward, and, as you jump, Lara will grab the ledge on the opposite wall.

Whilst on the rope, position Lara as in the screenshot to the left. Swing twice and leap to grab the second crack in the pillar.

Once you reach the second balcony and kill the gorillas, pull the switch and either drop down onto the floor, or into the water. Then make your way behind the Midas statue as you did before, and go through the door.

Once in the fire room, first pull the underwater lever, and then make your way back to the position as pictured in the first screenshot to the left. Draw your Pistols and start running forward. When Lara reaches the point marked with the yellow line, jump to land on the pressure pad, and then, with forward button pressed all the time, immediately jump again. If you're lucky, Lara will jump onto the platform in front of her and the flames won't start (as pictured in the second screenshot to the left).

To successfully jump onto the ledge behind, position Lara as shown in the screenshot to the left, turn around, and jump.

When you pull the switch and you have to return to this pillar, jump almost from the edge, but not too hard. Lara will grab the lowest crack on the pillar. She will start to slip, so be sure to save her before she falls in the water.