This mission will not be offered until you have met the following prerequisites:
1. Progress in the campaign until you have reached the Mission of San Juan. Once you are there, you can immediately fast travel to the Hidden City and begin the Path of Fear.
2. Complete the "Retrieve the King's Horn" objective of the "Hearts and Minds" side mission. This side mission is available soon after you discover the Hidden City. Uchu is the mission giver for this one. He is in the Skull Cave if you have progressed that far. If you haven't, he is in Unuratu's house.
Once you have completed these prerequisites, you can receive the mission by talking with Jonah and Uchu in the Skull Cave. The mission is available anytime thereafter, including after completion of the campaign.
The combat portion of this mission takes place inside Lara's head, so most of the regular gameplay mechanics don't apply. This means it doesn't matter what weapons and outfits you have equipped or what you have in your inventory. Most or all of your skills are irrelevant also. So, once you receive the mission, just do it and don't worry about preparing for it.
You begin the mission by walking into the pool at the north end of the Skull Cave and swimming through the opening at the end. Before long, Lara will have a nightmare. This is the combat portion. After that, you will have to solve the Howl of the Monkey Gods challenge tomb. That will earn you:
Once you solve the challenge tomb, Lara will be back in the Skull Cave. Report to Jonah and Uchu to unlock the achievement for completing the mission. You will also be awarded the Griff of Fear - White Knuckle
climbing axe and the Scales of Q - Feathered Serpent
outfit, which you will equip to unlock:
Please let me know in the comments if I left out something important. That would do more good for the community than an uncommented downvote would.