Relevant Talents used:

Void Tendrils
Mindbender
Desperate Prayer
Divine Insight
Divine Star

iLvl: 534

This is a three phase encounter that requires good dps (phase 1), survival (phase 2) and execution (phase 3). Overall one of the more challenging encounters I have soloed in a while. Yes, I could have waited a few more days for patch 5.3 so I can upgrade my gear with my 3000 valor points for an easier (a LOT easier) time with this boss, but I prefer the extra challenge brought on by lesser gear.

Phase 1: Onyxia
Basically ignore all incoming adds and burn Onyxia down ASAP. The goal is to kill her shortly (approx 10 seconds) after Nefarian lands. Any later is undesired as Nefarian and Onyxia will kill you (due to the haste buff gained from being close to each other). Any earlier is also undesired as the adds wouldn't deanimate all in the same place. The adds will deanimate shortly after Onyxia dies regardless of their remaining energy and it is important to have them all deanimate in the same spot. (This does become less important as iLvl increases, it is probably no longer important for a T15 BiS geared priest).

Animated Bone Warriors:
These are the adds that Nefarian summons in phase 1 prior to landing. These adds initially starts with 100 energy and slowly gains a stacking buff that increases their damage dealt (by 100%, 200%, etc). Their energy however, gradually depletes, and will deanimate once it reaches 0. Their stacking damage buff will also reset once they deanimate. However their energy levels will increase back to full if they get breathed on or comes into contact with fire on the ground.

Phase 2: Chromatic Prototypes.
Nefarian flies back into the air after Onyxia dies and all adds deanimate. The whole room fills with lava and a Chromatic Prototype add (approx 1.7M health) spawns on each of the platforms. The goal here is to kill all three adds. They each channel a raid-wide AoE that pulses for 30k per tick, which can be interrupted with Silence (but can only interrupt one, and has a long CD). Nefarian will also barrage you with shadow bolts that deal 15-20k damage. This phase is basically a survival check, but high dps is also quite useful to burn the adds down quickly. After two of these adds are dead it becomes a lot less painful so take that opportunity to do some damage to Nefarian.

Phase 3:
There are a few factors that can trigger phase 3, I know that kill all three Chromatic Prototypes is one of them, I also know that phase 2 has a timer and phase 3 will start when that timer runs out. But from what I've seen from my attempts is that there is a third factor. If Nefarian's health reaches below 80% he seems to automatically start phase 3. This is somewhat strange since there is an achievement that requires his health to hit below 50% before phase 3 starts.

Anyway phase 3 is all about execution, since managing the adds from phase 1 is crucial to completing the encounter (obviously less crucial if you have the gear to just zerg the boss down). Nefarian will reanimate the adds by casting Shadowblaze Spark, which creates a spreading patch of fire on the ground where the adds are. The fire will instantly restore the adds to 100 energy, reanimating them. Nefarian will use this ability frequently in order to restore their energy back to 100. Fortunately Shadowblaze Spark only targets the ground where the adds are so it is possible to kite the adds out of that area before the spark lands. Also note that the adds energy levels will also restore if they come into contact with the fire that has been left behind by the spark.
Nefarian will also frequently use Shadowflame Breath on the player. Adds that gets breathed on will also have their energy restored.
With all that said the goal of this phase is to manage adds so that their energy reaches 0 and deanimate in order to reset their damage buff. The damage buff also increases their movement speed so it becomes harder to kite once the stacks reaches high. This is where you need to pay close attention to Shadowblaze Spark timers and kite once it is coming. There are also two ways to avoid the adds getting breathed on. The first is to use Shadowfiend/Mindbender to grab aggro on the boss while you kite the adds. The second is to root the adds with tendrils while you tank the boss, facing away from the adds. There are downsides to both of these methods. When the adds are rooted they are vulnerable to Shadowblaze Spark and the two abilities often come within seconds of each other. Shadowfiend/Mindbender also have a tendency to turn the boss in several different directions which means that sometimes the adds can still get breathed on if the boss happens to be facing in the unwanted direction.
Typically aim to reset the adds twice. And when they reanimate the third time, just burn the boss while CCing them in any way possible.