Make sure you have at least 1 of any element Crystal before continuing.
As with most AF quests, from this point on no longer need to be Black Mage.
Grab any type of crystal and travel to any Crag (Holla, Mea, or Dem) or any Teleport Crystal (Altepa, Vahzl, Yhoat, Jugner, Pashh, Meriph) and trade the crystal that you have chosen to the teleport crystal to receive a Faded Crystal. Since the fight is in Xarcabard, the teleport crystal there is most convenient.
Travel to Xarcabard and head west to (E-8) and look for two ???. You want the one that's inside the gorge. On the "left", most of the way to the actual entrance of the castle. You do not want the one that's on a cliff with the torch. See the annotated map here for clarity.
There may be some Demon Pawns and Demon Knights at the ??? so be ready to fight, just in case.
Note: If you are doing this with 2 or more BLM's the ??? stays in place but there is a 10 minute time limit before you can trade and repop the Chaos Elemental.
The star tree saplings at the farm in the basement of Heavens Tower aren't growing very well. Doctor Shantotto and co. have ordered an investigation to try and solve the problem. Help them by bringing back a glowstone from the crevasse of Xarcabard.
SPOILER WARNING: Click here for additional details about this story line.