My advice would first be - check that everyone is doing their jobs properly. The group damage that can be taken when people are not killing the eagles or standing under the target of the storm is totally unmanageable - and I'm in near complete raid healing plate.
That obvious comment aside, I find overall throughput is your friend. Keep holy radiance off cooldown, blow Divine Plea + Avenging Wrath the moment you dip below 80% mana, keep the eagle target topped off the whole time, and hope like mad your group is awake. If you get it right, it's a short fight, so Chase's comment about not conserving mana stands. Throughput and reflex-triage is what you need.

Oh, duh, forgot to add - pretty much don't dispell. I've found people die during the time it takes me to try and get a stack off them. Dispell in the first, perhaps 15-30 seconds can be worth it, but after that I don't even try.

heh I don't know about not dispelling since that debuff increases NR dmg taken. i found the key to eagle boss is a) have no more then 2 in melee and b) managing the little brown eagles which hits for like 10 or 20K

If you have a hunter or a shaman in you group, ask them to put up Aspect of the Wild/Elemental Resistance Totem, it should at least make the nature damage a little smaller.