NOTE: Before even entering a game of Zetsubou No Shima, one player should have the Anywhere But Here! Gobblegum equipped.
Around the map there are four pedestals with a set of symbols on them. You will need to note the symbols on them, and approach the Temple of Nan Sapwe where you can read your challenges, and in the center are four red skulls with symbols under them. Pick up the skull with the symbols for each pedestal, and then place the skull down to begin a short mini-game where you defend the pedestal from zombies, spiders, and sometimes Thrashers.
The pedestals are located at the following locations:
1. In the spawn room:
2. Near the airplane trap:
3. At the bottom end of the zipline, near power:
4. In the room where you build the KT-4, near Mule Kick:
As you defend the skulls, going down or allowing the zombies to do enough damage will force you to grab the skull and place it down again. Once cleansed, however, pick the skull back up and return it to where you found it.
After each skull is cleansed, an electric burst will hit the Temple and a fallen tree will rise into the air, revealing a staircase.
Go down the staircase, and interact with the Skull of Nan Sapwe. Corrupted Keepers will begin to spawn and attack you. Simply survive long enough until they disappear, and you can pick the skull up.
With the Skull acquired, go into the bunker where the Purple Water is found, and across from it is half a poster on the wall. Pull out the skull, and hold the left trigger to mesmerize this poster and reveal the second half, and the rest of the Easter Egg can begin.