The Migratory Hippogryph only needs to be defeated once per party/alliance in order for all Dancers on the quest to get the second cutscene and the key item. Just be sure that everyone has examined the ??? at least once for the initial cutscene.
If someone has just defeated the NM, it may take a few minutes for the ??? to spawn another Migratory Hippogryph.
Navigate to the permanent key item menu and read the key item description.
Talk to Laila at (G-7) in Upper Jeuno to receive a War Hoop (you must examine your key item first in order to get the cutscene, and your main job must still be Dancer).