The way to get this achievement is somewhat complicated, but easy to learn. The first step is to open up the ritual area to the right of spawn where the four red skulls have spawned. Underneath where the skulls sit are specific Apothicon symbols. These four symbol sets never change their order, but each skull's symbol set changes each game. The four sets of Apothicon symbols correlate to one of four ritual altars around the map (whose symbols will also change each game). The skull whose symbols they spawned above correlates to one of the four altars. No other skulls with different symbols can be placed in any other altar with different symbols.
Once the altar with the correct symbols is located, place the skull with the same symbols into the altar. This will spawn multiple zombies out of green portals in the ground who have green mist emanating out of their bodies. These zombies will not attack players, but instead will only go for the active altar. These zombies do NOT reward players with any points. The skull in the altar must be defended for about 30 seconds from the green zombies. If the altar/skull takes too much damage, the ritual stops and the skull disappears until the next round. Once the ritual is successfully completed, the zombies with green mist will die and players will be rewarded with 500 points. Afterwards, pick up the skull which is not covered in red anymore and return it to its spawn slot. Repeat this for the other three correct skulls.
Once all four skulls and altars are successfully completed and returned to their spawn points, a new area will open up beneath the skull's spawn. This area contains the Skull of Nan Sapwe but it cannot be picked up yet. Hold "square" on the skull to spawn keepers who will either attack the Skull or the players. These keepers must be killed near the skull in order for it to collect their souls (like the Apothicon Eggs from Shadows of Evil), and the players cannot leave the room until the process is finished or otherwise. Once enough keepers have been killed, an audio cue will play and the skull can be picked up.