Inside the copper mill building, go to the first level. Locate the grate shown in the screenshot, past which there is a tomb entrance. You simply need to walk around the grate on the left side, where you find the spot to climb up. At the other side, jump down and approach the panel at the wall - it opens a way down (before you reach the one at the grate, you can open the Chest).
As you go down, before you reach the fork, on the left you can collect an Archivist map. Then, continue down and keep to the left side. A bit ahead, use the rope to zip down. Right afterwards, you walk into a flooded corridor - go left and follow to the end, where you find a Survival cache. Then, return up and take the right corridor. Walk past the obstacle and jump over to the other side - there will be a cart coming your down way and Lara will slide down to the lower level.
After you regain control, climb down the stairs and go left (in the corridor to the right, there is a Survival cache), go down and watch out for a trap in the narrow passage. Then, in the small room, you need to craft a molotov and throw it over the wall of water flowing from the pipes, to burn down the obstacles at the other side (throw it a bit "above" the wall of water. From the table, collect the Relic and jump through the "waterfall".
Finally, you reach the place shown in the above screenshot. Jump onto the projecting planks to the left and go left (inside the recess, there is a Document). Past the cart, you also find an Explorer satchel. Finally, ride down, where there is a camp.
Jump over to the other side and jump down from the container of stones. Thanks to this, you push down one of the carts. To do the same with the other one, climb up higher (here, you can find a Relic and a Document), and look at the mechanism on the left.
In the spot shown in the screenshot, you can attach a rope and release the cart. After you do that, turn around, towards the wall - you find a beam attached to it, over which you need to jump to the other side (on the right, there is a Mural).
Finally, attach rope to the cart, in the spot shown in the above screenshot. Return down and hang down from the container, which lowers the cart. Thanks to this, you can jump, from the nearest platform, into the middle, where you need to use a bottle, or a fire arrow, to set the obstacle on fire. Jump over to the other side and you see the path to the book, which you find at the level above. Read it to complete the Challenge of this tomb.
Reward: "Hawk eyes" skill (Lara's instincts allow you to spot traps).