This boss is rather challenging, even for a shadow priest of high item level. The main issue with this boss is the high damage from the 2 Val'kyr, each meleeing around 10k damage, hence large amounts of healing is needed. A glaring issue here is that the melee damage from the bosses does not trigger Masochism and hence mana is very tight, depending on how much critical heals can be obtained.

Before the fight starts, grab either a black or a white essence. This allows you to deal 50% more damage to the Valkyr of the opposite colour (and 50% less damage to the valk of the same colour). It does not matter which essence you grab. Also the 2 Valkyr has a shared health pool, so the damage done to one Valkyr will also deal the same damage to the other.

As soon as the fight starts, little black or white balls will begin to fill around the room. Make sure to grab as many balls matching the essence you have grabbed earlier. This will give you a stackable buff called Powering Up, which at 100 stacks will increase damage dealt to the valk of the opposite colour by a further 50%. At the same time, try to avoid the balls of the opposite colour as they will deal some light damage.
The start of the fight is a simple tank and spank phase. Approximately 45 seconds into the phase the first special ability will occur. The special ability can be one of the following:

1. Twin's Pact (Fjola Lightbane): A shield will surround Fjola Lightbane, followed by a 15 second cast of Twin Pacts, which heals the Valkyr for 20% of maximum health. The aim is to break the shield (takes a little over 100k damage) and then interrupt the cast. If your current using the black essence, just dps her down. Otherwise, you must change to the black essence first before doing so. Once the shield is down, use Silence to interrupt. However, whilst one of the Valk is using this special ability, the other valk will now dual wield, as well as gaining a damage buff, attack speed buff that can stack over time, as long as the cast is not interrupted. It is preferable to use shadowfiend to deal with the other valk while you break down the shield.

2. Twin's Pact (Eydis Darkbane): Same as above, except this time Eydis Darkbane is the one casting Twin's Pact. You will want to have the white essence whilst breaking her shield.

3. Dark Vortex: Eydis Darkbane will begin channeling Dark Vortex. If you are in white essence, you will take damage. However being in black essence at this time will allow you to not only absorb the damage but also increase the stacks of the Power Up buff. During this time, it may be wise to start kiting the other other valk away from the one that is channeling, as well as attempting to collect as much balls as possible so that Empowered Shadows can be reached.

4. Light Vortex: This works the same as Dark Vortex except with Light. You will want to be in white essence during this time.

From my experience, the hardest special ability to deal with is Twin's Pact, especially when the one casting it is not the one you are currently attacking. This forces you to switch into the other essence first before ramping up the damage from scratch. Without a cooldown, situations like this can easily spell a wipe.

That is basically the whole fight. A special ability is used every 45 seconds. Always try to build the Power Up buff to 100 stacks as soon as possible. Remember during Empowered Light/Shadows not only damage increases by 100%, it also makes Vampiric Embrace twice as effective. A single Mind Blast crit during this time can heal up to 15k health.