Welcome to the Blood Prince fight. From left to right, we have Prince Keleseth, Valanar and Taldaram. The gimmick of the fight is that only one of them can be DPSed at any given time. When your raid pulls the bosses, the first target will always be Valanar.
Valanar will have Invocation of Blood. What this does is that it marks who is supposed to be the killable target. It also causes one ability to be Empowered. When you start the fight simply DPS the boss. DBM will call out Empowered Shock Vortex when Valanar starts casting it. This is your cue to turn around and run away from him and anyone close to you. It deals damage but also causes a knockback if anyone is nearby. On 10-man this isn’t much of a problem but on 25 it can be. Just stay away from fellow raid members as much as you can during this time. Once the ability is finished run back and continue to DPS.
Invocation will eventually jump to a different Blood Prince so be ready for it. If it goes to Taldaram, here’s what you should do: just DPS. The only thing that’s special about Taldaram is that he casts a huge fireball on a random ranged target. The fireballs takes a little time to form above him before it actually moves, so whoever it’s on has time to get some distance. The farther the fireball goes, the less damage it deals. Normally you wouldn’t have to worry about this since it always targets ranged, but there’s a slight chance it will if there’s some distance between you and the prince (for example, during the transition phase of going from one prince to the next), so just watch out for it. Otherwise, DPS away.
Prince Keleseth is also a tank-and-spank. There are two things that you should never do if he’s the active target: don’t hit the purple orbs. At all. Second, watch your threat. Whoever is tanking him will be busy gathering the said orbs and will rarely be hitting the boss. This means you can out-threat him easily. Throw out a Tricks on that tank to help him out.
There’s one more thing to watch out for throughout the fight: the normal, non-Empowered Shock Vortex. This appears as a swirling sphere of white light that phases in and out while it’s animating, making it difficult to see. When DBM calls out that there’s one near you, you have a few seconds to move out of where you are before it appears. If you happen to be near it, it will knock you back. If you find yourself knocked back for no apparent reason, don’t just run back to your former spot. There’s a good chance that a Shock Vortex spawned there. Recognize it, avoid it.
TL;DR: Watch out for normal and Empowered Shock Vortex. Only one prince can be DPSed at any given time. Don’t touch the purple orbs. Run away from huge fireballs heading your way.