Relevant Talents used:
Body and Soul
Mindbender
Desperate Prayer
Divine Insight

From a soloing perspective, the heroic version of the Twin Val'kyr is no different to the normal version, aside from the increased health pool and significantly more damage. Therefore the normal mode strategy is also used here. For the normal mode strategy, refer to http://www.youtube.com/watch?v=DRqpbb6S72Q

Just like in normal mode, a defensive playstyle is used. Thanks to the buff in Flash Heals, priests can now survive the onslaught of the Twin Val'kyr (with an exception). However, spamming these Flash Heals are now a lot less mana efficient. Therefore it is preferable to have Vampiric Touch up on both targets for as much of the fight as possible.

Similar to normal mode, Twin's Pact is the special ability that is hard to deal with, especially when the bubble is around the valk of the same colour as the priest. Usually when this happens, I simply call wipe. That is not to say that it is impossible to get through it, just that it'll probably take more effort and resources than what it's worth. If the bubble is on the valk of the opposite colour, ie. the valk which takes increased damage from the priest. The the best strategy is to send Shadowfiend/Mindbender on the other valk while focusing down the bubble, and interrupt when the bubble is broken. Unless there is an emergency, the fiend should specifically be saved for this purpose. The other special ability is obviously more preferred, as it provides a free increase to your "Power" buff, as long as you are of the same colour as the valk that is casting it. This is the most effective way to gain Empowered Light/Darkness buff, which deals even more damage to the valk of the opposite colour.

The majority of the damage dealt to the valks during the fight, should come from spells that are cast during the Empowered Light/Darkness buff. Vampiric Embrace can be used during this buff for some free damage without the need to heal.