This is an arena style pvp fight.    Every CC is on pvp durations and will suffer from diminishing returns.  They are susceptible to all forms of CC that is applicable to them, except for Mind Control.   Also, they have an aura which reduced aoe damage by 75%, not not feasible to simply try to aoe them down like trash.

Here are all the possible npcs you'd face: 

Class	Alliance NPC	Horde NPC
Death Knight	Tyrius Duskblade	Gorgrim Shadowcleave
Druid (boomkin)	Kavina Grovesong	Birna Stormhoof
Druid (resto)	Melador Valestrider	Erin misthoof
Hunter (surv)	Alyssia Moonstalker	Ruh'kah
Mage (arcane/frost)	Noozle Whizzlestick	Ginselle Blightslinger
Paladin (holy)	Baelnor Lightbearer	Liandra Suncaller
Paladin (ret)	Velanaa	Malithas Brightblade
Priest (disc)	Anthar Forgemender	Caiphus the Stern
Priest (shadow)	Brienna Nightfell	Vivienne Blackwhisper
Rogue (shadowstep)	Irieth Shadowstep	Maz'dinah
Shaman (enh)	Shaamul	Thrakgar
Shaman (resto)	Shaabad	Broln Stouthorn
Warlock (afflic)	Serissa Grimdabbler	Harkzog
Warrior (arms)	Shocuul	Narrhok Steelbreaker

In 25 man you'll face 10 of them.   In 10 man you'll face 6 of them.    Typically it seems you'd get 3 healers in the 25 man, 2 healers in the 10 man.

The strat is very wide and varied depending on exactly what combination of npcs you get, and what your raid make up is.    What CDs, CC, interrupts, cleasnes, pvp ability, etc you can muster up.

The only constant is probably, interrupt heals, cleanse CC and stuff on your raid, purge/dispel their Heroism/Bloodlust, bubbles, bops, etc.      And watch your own raid to see what to protect and heal.   And Totem stomp, well no macro works anymore I think, have people manually do them.

Anyways, I'm gonna give a possible strat now.   Remember, this can be totally ineffective depending on what exactly your raid make up is and what NPCs you get.    CC whatever isn't the focus target if you can, possibly trading types of CC when DR is reached.   i.e.   When sheep is on DR, start fearing.    While the old fear gets sheeped.     Coordinate.

Note:  This post has the AI Threat mechanics of the fight:  /FactionChampions#comment-48124

First Priorities:

Disc Priest and Resto Druids.   

In either mode, I'd say take out 1-2 healers first.    The Disc Priest can also dispel your CC and also as a clothie have lower hp than any of the other healers.  Burn Disc priest first if he exists.    Burn Resto Druid next if he exists.   

The druid mostly hots everyone up, and thorns.    And as an elemental, he's susceptable to less of your CCs.  But he should be easy to take down as long as 2 healers isn't laying into him.

Second Priorities:

Resto Shaman, Enh Shaman, Warlock, Warriors.

If the resto shaman is your third healer, and you killed Priest and Druid, he can probably just be CC'd the rest of the way through.    You should be able to out dps 1 healer up esp if CC'd.    Otherwise, this is a decent 2nd healer to take down.

Once you have 2 healers down, picking off a dps should be on your mind.

Enh Shaman's biggest annoyance is that he Earth Shocks a lot, messing with your healers, and has those Grounding totems that mess up a lot of your casters/CC.

Warlock's Hellfire can cause havoc on the raid, plus he fears and dots.   Being a clothie he's also one with lower hp.    I'd recommend him after you got through the shamans.

Warrior Bladestorm can cause havoc too.   But he is kitable if you got someone capable of it.   Rotating disarms on him would help too.

Third Priorities:

Rogues and Hunters.

These two are mostly annoyances via pure dps.   Though they can rape you early, if they can be CC'd and get people their bops or something, you can heal through their burst.

Final Priorities:

Basically anything else.   Death Knights, Boomkins, Holy Pallies, Ret Pallies, Mages, Shadow Priests.

If you reach these mobs, as long as most of your raid is still up, you should have a kill.    You're over the hump, and the major threats are gone.

Almost whatever order you want.   In our attempts we've so far been leaving Pallies up, CC'd til the end.

That's all I can think of, good luck!

Hard Mode:

Well, they obviously hit harder and have more HP.  But, they've also equipped their PvP trinkets, are better at focus firing, chain CC'ing, and reactions with BoPs and dispels.  

In 10 mans, the tweak we did is instead of knocking off the 2 healers at first, we killed a healer, then a dps.   If that doesn't work, kill off a dps first, cause they are more lethal in this mode.   Again it largely depends on comp, killing off 2 healers like the old way can still work.

In 25 man, we firstly decide to start the pull with a DK doing Hungering Cold on all of them.   This forces them to all (hopefully) pop their pvp trinkets allowing you to CC.

Next off, we decided to kill 3 healers first and always.   We have interrupters (rogue/warrior/etc), one on each to do the kicks and stuff.    Everyone that can, try to totem stomp also.    Finally, more one on one situations for others like our DKs, frost mages, etc kiting their Warrior, DK, Ret Pally around.    Maybe even putting someone on Warlock / Mage to keep kicks on them.   Otherwise, CC whatever else you can.

Achievements:

Resiliance Will Fix it! -  Kill the enemy heroes within 60 seconds of each other in 10/25-player mode.

Heh, this seems hard.   I can only think of doing this with minimal CC, and split your dps among them and heal through the entire thing.    Possibly using AoE, well maybe more splash damage aoe things.