See Party Missions for general overview of party missions. Basically, you need to kill 8 Fury Griffons, then kill Fury Griffon Leader. Unlike Griffon field raid, there is no Griffon Egg. The annotated map below shows the approximate locations of the 8 Fury Griffons. (However, they can move about and be dragged by players.) Leave a comment if there are major discrepancies in the locations.
All Fury Griffons have the same skill sets (icy poke, jump slam) as field raid version, except they are more powerful. Each Fury Griffon has slightly different stats, ranging from L100 to L115. They have very weak defenses, but very strong attacks. Killing them is not as much a problem as surviving their attacks.
Scouts should stay out of the Griffons' attack areas, and prepare to revive any fallen characters. Use Magic Barrier from [Incantation] stance to gain 30% chance to ignore Griffons' area attacks. Melee attackers can tank it by using Ropera (90% negate magic attack at Lv.12) from [Rapiere] stance. Con Impeto from [Prelude] stance should help a bit as well. Their skills may cause [Confusion] status, which can be removed with Refresh Mind from [Tactical Assistance] stance. Elementalists should take advantage of their low Fire RES for maximum effect.
Once a griffon dies, there will be a zone notice, saying: There are [number] Griffons remaining. So run around the map, and hunt down all the griffons. Once the last griffon dies, there will be a zone notice, saying: Insane Griffon has appeared somewhere in Vegas Javier. Fury Griffon Leader (L104 Life) will appear at a random location. Find and kill it in the same manner as the lesser chickens.
See also クエスト/グリフォン 党.