Relevant Talents used:

Mindbender
Desperate Prayer
Twist of Fate

iLvl: 566

This fight is achievable as shadow with a 580 ilvl. But since I no longer raid, I don't foresee myself achieving that kind of ilvl any time soon. Even if I get to 580 ilvl, this fight still won't be anything more than a zergfest. However apparently this fight is quite achievable at a much lower ilvl if done as Disc, but it is still quite nerve wracking towards the end where everything becomes messy.

The Mechanics:
This fight is just one phase, with both a hard and a soft enrage. The soft enrage is that Ultraxion will deal 200k damage split between all raid members every 6 seconds, and this is reduced by 1 second for every minute into the fight. Soloing this fight means you take the full 200k damage. He also melees quite hard too. Fading light is a debuff that the boss casts frequently. The debuff will kill you when it expires unless you leave the twilight realm upon expiry. Pressing the extra action button will port you out of the twilight realm for 5 seconds or until Fading light has expired. Ultraxion can still melee hit you while outside the twilight realm.

The buffs:
The first buff available is gift of life from Alexstrasza. This supposedly increases healing done by 100%. Apparently this also affects Atonement just by having a quick look at the video of the fight.
The second buff is essence of dreams from Ysera. Every heal cast duplicates itself and the duplicate will split among all friendly targets. This is rather useless when soloing since there are no other friendly targets (except maybe Shadowfiend)
The third buff is source of magic from Kalecgos. This provides 75% reduced mana cost and increases haste by 100%. This is more desirable than gift of life at this stage as depending on the amount of spirit, going OOM or being close to it is a likely possibility by the time this buff becomes available.
Only one of the above three buffs can be active at any time.
The final buff called Timeloop will be given to you by Nozdormu. This allows you to survive a killing blow.

In general it is recommended to grab the Gift of Life buff asap, and then switch to Source of Magic when it becomes available.
The final minute of the fight can be really messy. Since the 200k raidwide damage happens once every second. Use all possible cooldowns to survive and hope to finish the boss before he finishes you.

PS. I always thought you could have all 3 buffs at the same time... until I started attempting this fight myself.