Step one: you must equip the related challenge (collect at least 10 artifacts) in the run you accomplish this goal to unlock this achievement.
Step two: spawn into the level, quickly open the chest in the back of the vehicle, and start running in a straight line anywhere. Make sure to pick up any resources you pass on the way. Eventually your map will update as to having found a tomb, great!
Press down on the right analog stick and look around to find the blue light showing where the entrance is and go to enter it. Before you fully commit to spelunking, make sure your food and heat are pretty high, exploring can take awhile, especially if you don’t have the skills that spot traps or see relics through walls.
Carefully make your way through the tunnels, checking for traps (pitfalls especially) and going down every passageway, even if you have to double back to get it.
On average you get 3-5 relics per cave, so you’ll repeat this process 2 or 3 times. Run straight, find cave, safely spelunk, get money$.
Afterward, you’ll need to find a pyre (the triangular piles of sticks) usually located in shelters or enemy camps, you might have seen some as you were running straight. Don’t worry if you’re in one of those places and you don’t see one yet, you have to stand very close to them to put them on your map. Then just light the pyre, defend the area (sometimes glitchable by quickly standing in a patch of grass and not moving) and jump on the rope to escape.