WoW.com's Guide to Blood Prince Council
The Blood Princes can be a difficult fight for many raids, forcing folks to move, react and adapt throughout the entire fight. The issue with the Blood Princes isn't that the individual parts are so difficult. The challenge is that the Council is actually three different fights that swap phases according to which of the San'layn is empowered at the time.
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Composition
For your 10-man raid makeup, you'll be aiming for two tanks. You'll want either two or three healers, with the rest of your raid being DPS characters. Whether you need two or three healers will depend on how sturdy your tanks are, as well as how awesome your raid healing is -- use your best judgement here. In 25-man, you'll need two off tanks and about twice as many healers.
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General strategy
The three princes share a single health pool, but it doesn't show up on all three characters at the same time. Instead, two of the vampires will be at 1 HP at any given time. Try and ignore that, even though you'll be tempted to blow your nukiest of nukes and finish him off. The two princes at 1 HP cannot be killed or damaged; your raid will have to focus on the vampire that has the full health pool. The Darkfallen Orb is what determines which of the princes is currently empowered, which also grants them special power boosts. The buff the princes gain while under the effects of the orb is titled Invocation of Blood.
The easiest way to understand the Blood Prince Council is to go prince by prince. You'll have a different tank and tactic for each prince. It all is happening at the same time. Let's start with Keleseth.
Prince Keleseth
Your ranged "tank" will be playing with Keleseth. I've seen death knights do pretty well tanking Keleseth, also, so if you're in a 25-man raid and have an "extra" tank, Keleseth might be a good assignment for them. His abilities aren't too difficult to handle, so it's largely up to you how you tank him. Ultimately, though, someone's going to have to keep him under control. If you're using a ranged DPS, most people seem to prefer warlocks.
Shadow Lance is Prince Keleseth's main attack. It inflicts about 16,000 damage in 10-man raids, but about 18,500 damage in 25-man raids. (It's obviously shadow damage.) If Keleseth is under the effects of the Darkfallen Orb, however, the Shadow Lance becomes the much more powerful Empowered Shadow Lance. If left unmitigated, the Empowered Shadow Lance will drop a whopping 80,000 damage on its target in 10-man raids and around 92,000 damage in 25-man raids. Assuming your tank doesn't have 100,000 hit points, you need to mitigate this damage.
The way you do that comes from Keleseth's next ability. He spawns several objects called Dark Nucleus. Each nucleus does a slight amount of damage to targets around it but also grants its target shadow resistance. (It does this by a power called Shadow Resonance.) The Dark Nucleus will die if you do too much damage to it, so your tank should do just enough damage on the nucleus to keep it firmly aggroed to him. The Dark Nucleus also spawns anywhere in the room; be ready to grab new ones as your Shadow Resonance falls off. You need at least three stacks to survive an Empowered Shadow Lance.
Prince Taldaram
Taldaram is perhaps my favorite of the three Blood Princes, given that he's also got the most obvious Twilight reference. (OK, maybe I should say I find him the most amusing.) Periodically, Taldaram will emit Glittering Sparks from his chest in an area in front of him, with a random raid member as his target. Anyone standing in the cone will be affected by the Glittering Sparks effect, taking damage and moving 20% more slowly.
Taldaram will also summon a gigantic ball of flame. The power he uses to do this is called, appropriately, Conjure Flame. These balls fly at their target and explode for significant amounts of damage. If Taldaram is currently under the effects of Invocation of Blood, the conjured Flame Spheres will also spark for additional damage to anyone nearby.
Like Keleseth's Shadow Lance, there's a trick to mitigating the damage from exploding Flame Spheres. Every time the sphere "touches" a raid member between Taldaram and the sphere's final target, the flaming ball shrinks a little bit. The more people it touches, the more it shrinks. So, when the sphere first targets a player, that player should move away and kite the ball. Other raid members should briefly touch Taldaram's sphere, absorbing a little bit of its power. This way, when the Flame Sphere reaches its final target, the blast isn't deadly enough to one-shot most classes.
Prince Valanar
Prince Valanar is mostly a physical powerhouse. He summons an object called the Kinetic Bomb, which is essentially a big bouncing ball. It starts up in the air and falls to the ground. When it touches the ground, it explodes and bounces back into the air. And it keeps doing this, rocking 10,000 to 13,000 damage each time. You mitigate the Kinetic Bomb, though, by hitting it with DPS. It absorbs this energy, causing the bomb to bounce higher in the air.
He also summons Shock Vortexes around your raid. This is the ability of Prince Valanar that is affected by the Invocation of Blood. The vortex will do damage to people who are standing around it, but also will afflict them a knockback. So, when you see the spell being cast, your raid should spread out to avoid hitting too many people with the power at once.
Putting it all together
Obviously, having three different bosses doing three different things at the same time can be very confusing for raids. You have to anticipate and react to all of the princes' abilities, or else you're just going to get tossed around by vortexes and blown up by Flame Spheres. Here's the quick and dirty:
You have three tanks. (If you're in 10-man, use a ranged character with a lot of hit points for Keleseth.) Each tank is assigned to one of the princes. They tank them, about as tanks normally do. The person on Keleseth, however, will need to be sure to be in a position to pick up the Dark Nuclei.
Once you're in position, you kill the bad guys. Your DPS is only effective against one of the princes at the time -- it's the one being empowered by Invocation of Blood. You can tell which that one is by looking for the prince with the most hit points at the time. They share that pool of health, however, so when you run them dry, they all die at the same time.
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Abilities
Keleseth
Shadow Resonance Summons a Dark Nucleus. The nucleus channels Shadow Resonance into the nearest target within 15 yards. This channel is what will allow you to survive Shadow Lance.
Shadow Lance Inflicts immense shadow damage to his target. Shadow Lance does 15k damage in 10-man and 18k damage in 25-man. Empowered Shadow Lance does about 500% of that damage when Keleseth has Invocation of Blood.
Taldaram
Glittering Sparks Hits players in a frontal cone with Glittering Sparks, inflicting 3.2k damage every two seconds over eight seconds in 10-man, and 4k damage every two seconds in 25-man. Also reduces the movement speed of the affected targets by 20%.
Conjure Flame Conjures a ball of flames that flies through the air toward the target and explodes on impact. The ball Flames to inflict 7,500 fire damage to all nearby players within 15 yards when the ball of flames reaches its target. As it moves, the ball of flames does fire damage to nearby players and shrinks in size. The more flames the balls discharges while traveling, the less damage on impact it will do. When empowered, the ball of fire will also Flare.
Valanar
Kinetic Bomb Summons a Kinetic Bomb. The bomb drifts toward the ground and explodes on contact. Every explosion sends the bomb back in the air and causes Kinetic Bomb explosion. Direct damage to the bomb causes it to return back into the air.
Shock Vortex Summons a Shock Vortex that does damage and knocks back players within 13 yards. When Empowered, Valanar will summon Shock Vortex near all players within 30 yards.
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Tank strategy
You may use a ranged tank in this encounter; however, that's not quite as necessary any longer. A single tank with sufficient armor and health (like a bear) could tank Valanar and Taldaram, leaving a single other tank to worry about collecting Dark Nuclei.
It's often easy to use a "ranged tank" with shadow protection (like a shadow priest or warlock) to handle Keleseth. That being said, death knights and paladins are also capable of collecting adds at ranged very easily, leaving all of your available DPS on whoever the kill target is at the time.
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DPS strategy
Don't stand in Shock Vortex. Put a pet on the Kinetic Bomb to keep it in the air. (The ball moves faster in heroic; however, it may require more than one in that mode.) When the conjured flame ball appears, tag that sucker for a second to keep it from exploding for huge damage.
Mostly, though, don't stand in Shock Vortex, and be ready to switch targets in a moment's notice.
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Healer strategy
This fight feels like a huge cluster, because mods will be screaming, players will be screaming and particles will be flying across the screen in rapid motion. The most important thing is to keep your focus, don't stand in Shock Vortex and keep your heals flowing. It's best to take a relatively central location (if you can), because the tank responsible for collecting nuclei will be moving all over the room. The less you have to move as a healer, the better off you are.
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Other resources
Advice from Blood Pact for warlocks who are Tanking the Blood Prince Council
Fox Van Allen's Twilight jokes for Bleeding the Blood Queen
Holy Paladin's 10-man healing strategy
I Like Bubbles with an invitation to the Ice Cream Social: Blood Prince Council
Mystic Chicanery on why Kinetic Bombs Suck
Scattered Shots on how to Hunt the Crimson Halls
Tankspot's written guide to the Blood Prince Council