Here's how to find them all.
Rise of the Tomb Raider's Challenge Tombs are optional, but provide some of the best platforming and puzzling in the entire game. The entrances are hidden, and can be tough to find, but completion of these levels will give you loot you won't get anywhere else. They're worth the effort.
Below you'll find instructions on how to find the entrance to every Challenge Tomb in the game.
Glacial Cavern tomb
The first tomb's easy to find. You go right past it on your way through the Glacial Cavern. Just jump over to the location on the map below and the Ice Ship will be hanging from the wall directly in front of you.
Soviet Installation tombs
The Red Mine
The Red Mine is accessed through the Copper Mill. You'll finish a section in which Lara learns to make Molotovs. Once you've done that, climb a small set of stairs and look behind you. You're looking for the ledge in the image below. The location is on the map.
Jump across then turn to the left. You'll see some yellow symbols and a green light.
Drop down, walk up to the console and hit it. The door will open. Walk in to start the tomb section.
Voice of God
Go to the location on the map. You'll see a cave entrance.
Go inside the cave. You'll find a door Lara can only access once she's got rope for her arrows. Just pull the wood away and open the door with your ice axe. Walk in and start the tomb section.
At the location on the map below, you'll find a boarded hole in the ground. The only way to smash through is to shoot a block holding a log dangling above it from a crane. You can see the crane in the image below (sorry: I dropped the log before I captured the shot).
Now climb down into the cave using the ladder. You'll see the tomb entrance at the bottom, ahead of you and slightly to the left. Go in to start the tomb section.
Geothermal Valley tombs
House of the Afflicted
From the Valley Farmstead’s Base Camp, head north, cross bridge over the river, swing over the break in the path and you should find yourself at the location on the map below. You'll see an iron door and a low hole in the wall ahead. Move forward and crawl into the hole.
Once you've killed the wolves on the other side, open the door.
Walk inside and turn to the right. Follow the passage and you'll see the message letting you know you're entering the tomb section.
Baths of Kitezh
Find the cave at the location on the map below. Go inside. Find the bear. Run back outside before it eats you for lunch.
Kill the bear. This is easier said than done. A shotgun to the head works well, but definitely be prepared for some well-timed dodging.
Once you've killed the bear (don't forget to skin it!), go back into the cave and use Survival Instinct to show a weak wall at the back. Smash it with your ice axe.
Now go through into some water. Use Left Trigger to dive down under a wall. You should see the notice saying you've entered the tomb area when you come up on the other side.
Catacomb of Sacred Waters
From the Aqueduct Ruins camp-fire, look for a cave to the east. It's at the location below. You access the cave by jumping over from a fallen log.
Once you're inside just run forward down the passage. After a minute you'll see the note saying you're entering the tomb area.
The Pit of Judgment
Go to the location on the map. You should be facing a waterfall. Swim underneath and climb out behind it.
Turn left. You're now looking at a series of stairs.
You'll find the tomb entrance at the top. Go in and follow the passage.
Swing over a gap and then squeeze through a hole in the wall. On the other side you'll discover a new camp-fire and see the notice that you're now entering the tomb area.
The Lost City tomb
Chamber of Exorcism
This is the final tomb. Go to the location on the map. It's right on the east side of The Lost City. You'll see the cave entrance in the wall behind two ruined pillars.
There's a bear in the cave. Waste it, skin it, send it to bear heaven.
Click the right stick and bring up Survival Instinct. Smash the weak wall with your ice axe.
Just run down the passage. You'll soon see the message saying you've entered the tomb area.