Relevant Talents used:

Mindbender
Desperate Prayer
Divine Insight
Divine Star

iLvl: 523

Yorsah'j the Unsleeping is probably the easiest Dragon Soul boss to solo, so I'll be starting with this one.

Void Bolt:
Void Bolt is the "tank swap" mechanic in this fight. It's a stackable shadow DoT that increases in damage, lasts 13 seconds, and refreshes at around 7 or 8 seconds. My original strategy to deal with this was to use Mindbender to reset the stacks, however this did not work out for two reasons. Firstly my Mindbender for some strange reason, dies pretty much as soon as I set it on the boss. It lasts no longer than 2 seconds. Boss seems to be 2 shotting it. Secondly, a new stack of this debuff is applied BEFORE the previous stack has reached halfway through its duration. This means that the Mindbender must eat 2 stacks for me in order to reset my own stacks, but since it only lives for about 2 seconds, the most it could do is to eat 1 stack for me, which is still better than nothing. With resetting stacks out of the question, it does become harder on the healing, but still tolerable with high enough gear.

Oozes:
The main feature of the encounter. Yorsahj will begin channeling 3 different coloured oozes (from 6 different possible colours) towards himself. When an ooze reaches the boss, it will give him a buff depending on its colour. While the colour of the oozes may appear random, there are in fact set combinations of different colours that can appear. These oozes are attackable and can be killed, but you are only permitted to kill one of them. Therefore it is best to kill the ooze that gives the boss the nastiest buff rather than one that gives him a useless buff. Note that during the channeling is also the time for the much needed reset of the Void Bolt stacks.

Kill priority of oozes from a Shadow perspective:
1. Black -- This will cause boss to summon around 10 adds. Together, these adds cause just about as damage as the boss himself. Very painful indeed. Pop a potion and Mind Sear/Divine Star if this does happen.
2. Blue -- Drains all your remaining mana and stores them in a mana bomb with 1 million health. The drained mana will be restored once the mana bomb dies. The problem is, how do you kill it when you have no mana? If Black and blue appeared together, kill the black one since it has higher priority and use Dispersion after the mana drain. If for whatever reason Dispersion is on cooldown, kill blue and AoE the adds with a pot and other defensive cooldowns.
3. Yellow -- This will cause boss to attack 50% faster, as well as using his abilities generated by buffs from other oozes twice as often. Nasty but tolerable.
4. Red -- Gives boss a fire attack that deals more damage the further away you are from him. As a priest you are mostly face tanking at melee range, so this is not a problem. Only deals around 20k damage at melee range.
5. Green -- Gives boss an ability that deals massive damage to people who are stacked together. Hence there is no danger from this ability when soloing. Deals around 20k damage when not stacked.
6. Purple -- The most hated colour back then is the now most useless colour. The purple ooze literally does nothing. Purple is supposed to provide a debuff which, after receiving 5 heals will trigger an explosion, dealing massive near fatal damage to everyone in the raid but not to yourself. Since there is nobody else in the raid when soloing, you can heal as much as you like.

2-shotted this boss. First attempt was a blind attempt and my Fraps wasn't turned on. I deliberately had to stop my first attempt at 30% because Fraps wasn't on and there were no signs of wiping.