Attain Rank 5 in all Undead Nightmare Challenges.

There are 4 Undead Nightmare challenges:

Undead Sharpshooter
Undead Hunter
Four Horses of the Apocalypse
Undead Treasure Hunter
The location of the horses:

Pestilence is found somewhere in between Tall Trees, Manzinita Post, and Aurora Basin.
War is located somewhere between Benedict Point, Tumbleweed and Gaptooth Breach.
Famine is located somewhere between Chuparosa and Tesoro Azul.
Death is given to the player after completing the main story, though may also be found in Mexico.

Undead Hunter:

To kill bears, wolfs and cougars with a torch, take the horse Pestilence as it can't die. Cougars are often found west of Torquemada and in Tall Trees, bears can be found in Tall Trees and wolfs can be found pretty much everywhere.

Undead Sharpshooter:

Rank 3: Equip Phosphorus bullets and make 5 headshots.
Rank 4: Go to El Presidio, as 2 of each spawn there.
Rank 5: Best way is to go to El Presidio, and execute (move close and press without aiming) the zombies.
Undead Treasure Hunter locations [ Register or Signin to view external links. ]

To find a treasure map, find a chest at a random encounter which involves a camp.
Far north of Hennigan's Stead, in a cove. You have to move outside the borders and high into the mountains.
South east of Armadillo.
At the south-western edge of New Austin.
South-east of Las Hermanes.
West of Casa Madrugada.
View the video below for the locations of each treasure: