The petitioner on this hunt is Dania from the Nomad Village in Giza Plains. She stands in the Cockatrice enclosure. The Clukatrice appear west from the village, but the only way to make it appear is to kill every single mob there is in that area then leave it and re-enter. You should see a rolling yellow ball - it's a chickatrice - cluckatrice will come to you when you approach it.
+ 4x Chickatrice
about 7000 HP
Resistant to Libra
Except for the Cluckatrice you'll have to face four of its descendants.
The Cluckatrice itself uses two attacks: Muscus which slows one of you heroes down and Stone Gaze, which petrifies one of your heroes. First focus on Cluckatrice and after you're done with him take care of the four chicks. Personally I have killed the Cluckatrice with a quickening combo and then draw all chicks in one place and attack them all at once with Dark.
Bounty: 1000 gil, Jackboots, Rainbow egg