There are various setups that you can play with when doing this particular BCNM, as shown by the posts below. I'd like to share my own experience as to how to beat the mobs with the (tweakable) party setup I had:
BRD/WHM
BST/WHM
MNK/WAR (tank, which was me)
With both the BST and BRD subbing WHM, we didn't need an actual WHM. Right as we entered the battle arena, the BST cast buffs and both he and the BRD ate apple pies. I, as the tank, ate boiled crab (enhances defense). BRD sang +DEF songs while I boosted. Then, BRD engaged the left Furies by sleeping them, while BST used 2hr (Familiar) after charming the Furies on the right. I didn't do anything until Coco was half-dead while fighting the charmed Furies. Then, I charged in and engaged Coco while the BST and BRD healed me, and killed him. Meanwhile, the BRD kept the Furies slept using Foe Lullaby.
Then, we had the two Furies turn on each other (yes, we killed Coco first). When the BST's pet died, I 2hred it (you don't have to, depending on how much HP the remaining Furies has left) and {Hundred Fists} took the bats out in a flash. On our first success, an astral ring dropped. ^^
Tips for success: DON'T panic when the first sleep or first charm doesn't work. Keep at it, cure yourselves, it WILL work. I remember our third time when Charm must haved failed three times, but as long as the BRD kept himself healed, everything still went fine. I didn't voke the Furies after sleep/charm didn't work b/c due to my party setup, there wasn't enough MP to heal me AND keep my half-mages healed as well.
Good luck! May astral rings drop for you all! ^^
Edit: I had said that I zerked *AND* boosted during the fight, but I forgot that this BCNM has a lvl 20 cap to it. ^^;;
Edited, Sat Apr 2 01:29:04 2005