In Shadow of the Tomb Raider, in The Hidden City, you'll find 3 tombs of challenge. They are located in different locations, most of which you'll discover while performing your main missions.
Temple of the Sun
The Temple of the Sun is located near the Village Caves camp site. These are objects located in the southern part of The Hidden City.
To get to Temple of the Sun you have to break through the entrance with your axe. Then follow the path straight ahead until you reach the cliffs. You have to move on them using your axe and rope. Your task is to get to the other side first, and then move left on the rocks.
When you get to the left side of the location you will see an entrance to the cave. It is very visible because it illuminates in orange when exposed to light.
After entering the room you can look around - you will find a mural and two treasures that will allow you to learn the dialects. However, in order to go further you have to jump on the ladder on the left side of the room.
Going further you will find yourself at the entrance to the next room. You have to jump on the climbing wall and drop from it on the rope.
On the right side of the room you will find barely open doors. You have to approach them and squeeze under them. You'll find a puzzle with mirrors.
Your first task is to move the first mirror to the left. When you hit the green element, the shelf will move. You will be able to move to the other side of the shelf.
Position the second mirror as in the screen above. This will move the next shelf. Return to your first position.
Position the first mirror so that the light beam falls on the shelf on the right. Then move on to the very end of the object.
Set the next mirror in such way that the light falls on the left column. This will allow you to return to your original position. To jump on the shelf you have to enter the wall and jump on the object.
Adjust the first and second mirrors so that the light falls on the first column. Then return to the first position and set the first mirror again.
Position the first mirror so that the light falls on the third column. We've presented this in the screen above to make it easier to determine the position of the column. Then go back to the second mirror.
Jump to the end to the right side of the location. Position the mirror so that it falls on the nearest column. Next, return to the rocks between the second and third mirror.
Now jump to the object shown in the screen above. From there, go to the left until the end of the object. This will take you to the chapel.
You will get a Hoatzin's Hunger skill. This skill increases the amount of natural materials collected from one place. It is not possible to further develop this skill.
Ancient Aqueduct is a tomb located near Upper City. You will come across this tomb on main missions. To get to the tomb you need to wear a Serpent Guard suit.
To get to the tomb you have to swim under water. When you dive, keep with the path, don't change it, and you'll get straight to the next room. There you will be able to go out on a rock shelf.
Climb up the rock shelves to the top of the cave. This way you may enter the cave. There is a monolith here that will develop your knowledge of the MAM dialect.
At this point there is a small game bug. When you go further Lara suddenly stops and gets rid of her equipment, she only has a bow left at her disposal. Don't worry about it and go further. A moment later Lara will stop again, this time in order to pick up all of her equipment. This way you will be able to use all your weapons.
Jump from the rocks into the water and swim to the other side of the room. There, you will get to the riddle. In the following section of this guide we've described a detailed guidelines that will help you in raiding this tomb.
Your first task will be to start the machine on the right side of the cave. Go to the machine and pull it. This will fill up the water reservoir. Then you will be able to pull one of the rafts floating on the water. All you need to do is to shoot the rope with your bow and Lara will quickly pull the board to herself.
Your next step is to jump into the water. There, you will find a gate on the left side. Open them with your axe. This will lower the water level and let you to drag the raft to the next gateway.
Connect the spool on the gates and the one on the raft with a rope. Then return to the machine and start it. This will fill the water reservoir again and the gates on the bottom will open. Jump into the water and swim quickly to the other side of the cave.
Underwater, swim to the left. There you will find yourself in a closed passageway. You will open it with your axe. When you get through the passage, swim to the surface.
While underwater you have to open the gate, again with the help of your axe. This way the water level will decrease and you will be able to open another passage with the help of your bow.
When you open the passage a dozen enemies will appear. You have to kill them all in order to move further. It's best to kill them with a shotgun - they run so fast that it's hard to shoot them with a bow.
Your next task will be to pull the raft to the other side of the cave. To do this, you need to shoot a pair of accurate shots at the rope knot, and Lara, using her own muscles, will pull the raft to the other side. When you do this, return to the machine and fill the tank with water.
When the tank is filled with water, jump inside, stand on the raft and jump out of it into the open passage.
As you move to the next room, a bunch of enemies will attack you. Kill them and head upwards. There, run another machine to pour water. When you do this, the machine will break down and more enemies will spawn. In order to move further, you have to kill them.
Your next task will be to connect a rope on the raft with the rope near the mill. When you do this, climb on the rocks near the mill.
From there connect successive ropes with each other. On the screen above we've presented which object should be attached to the previous element. When you do this, a few enemies will appear and cut the ropes to destroy the path. You have to kill them and then repeat the whole sequence. When you reconnect the ropes you will be able to go to the other side with confidence, cause you won't meet any opponents this time.
From this challenge tomb you will get the Jaguar's Paw skill. It increases the probability of knocking down an enemy with a melee attack.
Path of Battle
You can unlock Path of Battle tomb by completing the Hearts and Minds side mission. There is no other way to get to this tomb.
To enter the tomb dive through a gap underwater. Swim along the path until you find some sharp traps. Dodge and pass through them.
When you get out of the water, jump on the wall. Descent on the rope from it. If you jump off it without using the rope, Lara will die on the spot.
You find yourself on a shelf with a camp. There, on the right wall, there is a passageway. Lara must squeeze through the traps.
On the other side you have to use a machine. It will activate the traps so you may pass freely on your way. Jump on this road, run to the other side avoiding all traps. On the other side, trigger another trap, which will also allow you to cross the road.
A big trap will appear. It's locked so you can't enter it. You have to run to the right side of the trap, activate the machine, move through small traps and start the machine in front a large trap. After a successful sequence, do the same on the left. If you do the job correctly, the trap will stop and you are finally able to climb up to the chapel.
From this challenge tomb you will get the ability of Sip's Quiver. This skill allows Lara to shoot 3 arrows with her bow, without taking the arrows out of the quiver.