Trade 7 or so stacks of crystals to one of the gate guards, or repeat Mission 1-2 10 times.
After accepting the mission, report to Halver who will send you to the king.
After the cutscene with the king, be sure to bring along someone who can cast Sneak and Invisible on you, or purchase several Silent Oils and Prism Powders, and start gathering the first two key items. The key items must be obtained in order.
Once both key items have been obtained, go to Jeuno and get a full alliance of level 65+. Make sure everyone has Sneak or Silent Oils.
Take the southern Eldieme Necropolis entrance from Batallia Downs. Head to the southern room of Eldieme and drop down the center hole at G-9. Once you land, head east and you will be on a new map. Just head south, taking a right turn at the first intersection and a left at the second intersection.
After you zone into Batallia Island, take a right turn towards the stone monument. If Ahtu is out, defeat him first.
Once everyone is ready, inspect the ??? that is located on a cliff. This will spawn 2 Greater Bird type NMs:
Suparna: WAR type NM; Special Attacks: Horde Lullaby, Mighty Strikes
Suparna Fledgling: WHM type NM; Special Attacks: Horde Lullaby, Massacre Elegy, Giga Scream, Dread Dive, Benediction.
Have a RDM put Gravity on Suparna and take it for a walk on the island, as the greater birds will not sleep (both birds will not resist the other debuffs, however, but they will not last long). Everyone else needs to concentrate on the Fledgling. Both birds will use the 2hr abilities of their jobs. Suparna, although it hits around 200 to a non-tank, must be kited due to Horde Lullaby threat. Once Suparna Fledgling dies, focus efforts on Suparna.
Alternatively, you may have everyone stand at the opposite end of the island while one person spawns the NMs (preferably a job that has Utsusemi, Stoneskin, or Flee). That person will have to run them to the zone-line, while the main tank provokes the Suparna at the cave-mouth and runs it to party. Only one NM has to be defeated to complete the mission.
If only one NM is pulled, a NIN75 and RDM75 can easily duo this fight.
Once both birds are defeated, everyone will need to inspect the ???.