Trade 8 stacks of crystals to one of the gate guards, or repeat Mission 1-2 10 times for the necessary Rank Points to get the mission.
After accepting the mission, zone into Northern San d'Oria for a long cutscene. At the end of the cutscene, zone into the castle for another cutscene. During this cutscene you will be given orders to head to Qu'Bia Arena.
Now gather a full party of level 70+. Only San d'Orians that have previously done the mission, or are currently doing the mission, can enter the BCNM.
Having a mage that can Sleepga is useful for this mission. Sleepga II is not necessary as these Orcs will fall quickly to a level 75 DD job.
Enter Fei'Yin, watch a cutscene, and proceed to Qu'Bia Arena. Once the party is ready, enter the uncapped BCNM.
Upon entering the BCNM, an event will begin. Once you appear in the battlefield, cast your pre-fight buffs.
Next it is imperative you silence the Warmachine. Strangely enough, that hulking thing is actually a White Mage and will cast Curaga quite often, waking the horde up and causing problems.
As such, kill the Warmachine first, Ranger second then pick off the remaining orcs. It does not matter on which orc you do next after the RNG is dead. They are easy prey.
Keep a weak one alive and slept and rest to full. Killing the final orc will trigger an event.
For Part 2, Prince Trion will join you. Mages must keep him alive, as if he falls, your party will be ejected from the battlefield. Prince Trion will not wait, so follow him. (Edit: Trion did not engage, so we had time to buff a little) This part of the BCNM will consist of 3 Orcs:
The desired order should be BLM - PLD - DRK. However, Trion will randomly attack one of them. The tank should engage the PLD (as he will simply resist sleep) and the DDs with provoke should go after whatever Trion goes with. If you get lucky, Trion will go after the Paladin helping you immensely. The Red or White Mage should be focused on silencing everyone, though the Paladin will prove difficult to silence while the Black Mage sleeps whatever is not being engaged at the moment. The Red or White Mage should keep Trion alive for even though he's a Paladin, his attached AI isn't all that intelligent. Once all three orcs are dead, another event will occur.