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 health point at any given time. Try and ignore that, even though you'll be tempted to blow your nukiest of nukes and finish them off. The two Princes at 1 health point can not 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 are 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.
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 resist. (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.
Taldaram is perhaps my favorite of the three Blood Princes, given that he's also got the most obvious Twilight reference. (Okay, 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 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 do 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 they're in a position to pick up their 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 that being 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.
Good hunting out there!
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