Basic mechanics for soloing:
As the mechanics in TK are still very important, there are some mechanics when soloing you don't want to ignore.
P1: No class at 90 should have any problem with adds; the advisers abilities are trivial one at a time.
(If healing is a problem for you class, kiting Thaladred is a good idea. If you let him smack you, it may be a good idea to pop a bubble type defensive CD to neutralize the debuff after he's dead.)
P2: Again, should not be a problem at 90. If your DPS is on the low end and you have trouble with P3 starting before the weapons are down, make sure you're interrupting the Cosmic Infuser's heal. Other than that they can be AoEd down very fast. The only weapon worth equipping still is the Staff of Disintegration: it will protect you from stuns for Telonicus as well as disorient from Kael'Thas. (Remember that you must equip the weapon and then use it for the buff.)
P3:This is the phase where things start to get messy. The advisers' abilities all together are a real nuisance, you will have to prioritize the four adds on this one or you will be CC-locked.
Grand Astromancer Capernian: She will cast a 10 second Conflaguration on you every so often. She also has the least amount of health among the advisers. When soloing, she should go down first. (melee will want to attack her with their backs to a wall as she does have a knockback that slows)
Thaladred the Darkener: He hits by far the hardest and will silence you in melee range. He can be kited and saved for last, as he walks, rather than runs, but due to his damage output, I recommend killing him second. (He does have a knockback, which can help if you want to kite him.)
Master Engineer Telonicus: He will maintain a debuff that randomly stuns you for 4 seconds
(There is no GCD on this, so it is possible to be stun locked indefinitely, however implausible). Depending on how you plan on soloing this, determines his priority.
Lord Sanguinar: Once in a while he will fear you for four seconds. At 90, his damage is trivial and is not a significant threat.
P4: Kael'Thas will become targetable and you can now work on him. Alone, you do not have to worry about MC, as he does not MC the tank. However, he can still hit fairly hard so this phase is when you want to pop CDs (offensive and defensive)
Pheonixs should not be a problem if they are killed as soon as they spawn (as well as their eggs). If left alone their AoE will add up, and if multiple pheonixs are up, this will add an unnecessary amount of damage.
Flame strike is another unnecessary damage causer. Simply step out of the large red circle.
If healing is a problem for your class, interrupt Pyroblasts (silence works best, he will cast three in a row)
Silencing him will cause him to melee which does relatively no damage.
P5: At 50% health, he will return to his spawn point. (He may cast another disorient or MC between phases)
When he returns to the ground and becomes targetable again he will throw you into the air. If you touch the ground you will be forced back up. Fly down to around his head height and begin to DPS.
When he casts netherbeams you will want to back up. It lowers you max health by a percentage each , if he gets enough stacks on you he can easily one shot you.
He will continue to spawn pheonixs but while in the air, their AoE won't hurt you; so unless you have nothing to do, you can usually leave them. His flamestrikes will also miss while you are airborn.