Relevant Talents used:

Body and Soul
Mindbender
Desperate Prayer
Divine Insight
Divine Star

iLvl: 504

This boss is a DPS check, and given the 5 minute enrage timer (usually berserks at 4min 55sec) and 23.6mil health, you will need 80k DPS to beat it. This should be quite manageable in heroic T14 gear.

Dealing with Searing Shadows:
The only major mechanic to deal with is Searing Shadows, which is a frontal cone breath attack. It will deal around 100k shadow damage and applies a stacking debuff that increases shadow damage taken by 100% per stack, effectively making the next breath more damaging. The debuff lasts 30seconds but the breaths comes every 20 seconds, so resetting stacks can be a challenge. Traditionally tanks reset this debuff by taunting the boss off each other and taking turns on the debuff, but from a soloing perspective, the only way to lose the debuff is to somehow drop aggro onto something else, like a pet or a cardboard assassin, or perhaps an immunity cooldown. Usually, no cooldown is required if taking a breath without any stacks. When taking a breath with 1 stack, cooldowns should be rotated. Mindbender should be available to take every 3rd breath so stacks should never go higher than 2.

Healing:
The boss melees for anywhere between 35 - 55k non crit, sounds nasty but usually a combination of PoM, PW:S, Renew, Divine Star and Devouring Plague should be adequate. Flash Heal should be avoided if possible due to the tight enrage timer, especially for T14 gear. T15 and onwards should be a lot more lenient though I cant say I'm optimistic about shadow's incoming blanket healing nerfs.