The main reason why people are killing Kael'thas in The Eye every week is for a chance at the Ashes of Al'ar. If you don't care about the color and don't like the low drop rate, Reins of the Dark Phoenix is a similar mount. Read on for Kael'Thas guide.
Entrance to The Eye/Tempest Keep
The Eye is located in Netherstorm, so take the portal to Shattrath or the portal to the Blasted Lands (closer option) and fly north. You'll see some floating structures once you get to the right area, the one you want to go to is the biggest one, floating lowest to the ground. Once inside, you'll have to kill a few packs of trash to get to KT, they shouldn't be a threat. While you can kill all the other bosses for transmog items, you can also skip everything and go straight for Kael'thas. Refer to the map at top if you don't know which room he's in.
Start the fight by running up to the platform KT is on, he'll have a speech and then his advisers will activate one at a time and try to kill you.
Thaladred the Darkener will silence you and put a bleeding debuff on you.
Lord Sanguinar will cast a fear that lasts for 4 seconds and hits everyone in 35 yards.
Grand Astromancer Capernian will disorient you for 8 seconds with a conflagration, knock you back with arcane burst.
Master Engineer Telonicus will randomly stun you for 4 seconds if he puts Remote Toy debuff on you.
They all don't have very much health.
KT summons 7 weapons, they can be looted once they're dead. The only one that matter, if you can use it is the Staff of Disintegration.
All the advisers revive and attack you at the same time.
Phase 4 100%-50% HP
KT attacks you, and summons phoenix (which won't do a whole lot to you at 90), and mind controls if there's more than one target. It's important that you dismiss your pets during this phase unless you want to risk resetting him. Blood DK blood worms can cause him to MC you, so go frost.
He'll float in air and summon nether vapors, which are black clouds that will debuff you and take 10% of your max health per stack.
What to do
This will depend on if you can use a staff or not. If you can't use a staff, kite all the adds very far outside of this boss room so that they do not all reach you at once and cc chain you until you're dead in phase 3. If you're confident in your killing abilities, feel free to kill them all on the platform and use whatever cooldowns to kill the advisers in phase 3.
Aoe the weapons down, pick up and equip Staff of Disintegration if you can use it. Right clicking the weapon will activate the aura that makes you immune to the Adviser's CC. If you can use the staff, you can just kill the advisers quickly and not worry about kiting them far out of the room in phase 1.
Kill Capernian first, then Thaladred if you're a caster, then Telonicus and Sanguinar, or whoever reaches the room first if you kited them out. If you have pets make sure they're dismissed at the end of the phase so KT doesn't mind control you.
Burn Kael'thas hard, you have enough health to ignore interrupting his pyroblast and his phoenix.
Burn him some more while avoiding black clouds.