Relevant Talents used:
Body and Soul
First solo kill of patch 5.0.4! The priest has received many class changes, which are both good and bad for soloing, but I am not about to get into that here.
The encounter is divided into 3 phases. Gormok, Twin Jormungar and Icehowl. Gormok is the toughest one for casters, especially one without a pet. The Twin Jormungar is significantly easier, and Icehowl is the easiest (to the point that it is a complete faceroll).
Despite Gormok having a Impale debuff which stacks every 10 seconds, dealing higher damage each stack, it is actually not a good idea to nuke it down ASAP. This is not to say that you should take your time, but you should be saving the 3 orb DP for snobolds. As those adds are the most annoying part of the fight. There are 4 snobolds to deal with in total, and each time Gormok throws a snobold at you he will gain 15% increased damage. so definitely use defensive cooldowns sparingly and wisely. He will throw a snobold every 15 - 20 seconds, which is not enough time to accumulate a 3-orb DP, so Divine Insight and SW:D will be greatly useful.
The Twin Jormungar Acidmaw and Dreadscale are a lot easier. Begin by DPSing Acidmaw, but also put VT on Dreadscale for that extra mana (if needed). When infected with Paralytic Toxin, the only way to clear the debuff is to also have Burning Bile at the same time. Once Acidmaw is down, Dreadscale will gain a soft enrage but it really isnt anything to be concerned about.
Icehowl is simply faceroll. Keep health high as he periodically stuns for 5 seconds as well as knockbacks. Also when he does Massive Crash, run out of his way to avoid being charged at. As a result he will become stunned and take double damage for a short period.