Long live the King!

Finally! Definitely my most technical soloing ever. Not to mention the 600+ tries, and about 250 scrolls/food/drum charge, dozens of potions... Cost me the price of 6 or 7 naxxramas farming runs. But it was definitely worth it, since it was the boss I absolutely wanted to solo before Pandaria.

Video: Durendil vs the lich king

Now for the guide:
I won't be going over the lich king's abilities, so check wowhead/wowpedia if you don't know him.

Phase 1:
The main thing is to deal with the adds, the plague and the infests.
Tank him on the edge: that way, shambling horror will spawn in multi-shot range from the lich king, although it may not be true for the ghouls. And make sure you have a passive button close at hand, to put your pet back in place.

For the adds: one out of two spawns of ghouls will be followed by a shambling horror. Wait until all three ghouls are up, then feign death misdirect and multi-shot two times, with one action or two between the two. Basically, it's either multi/steady/multi or multi/chimera/multi or multi/chimera/mend pet/multi. But no multi/steady/instant/multi, misdirection will fade before that. If a shambling horror spawns, make sure you multi-shot after it spawns. You will want to give the first necrotic plague to an add, but not the others, or they die too quickly.

Pet survival: not really an issue as long as you never leave two enraged horrors up. Make sure you have a macro to dispel a horror (however, it will only dispel the nearest horror - check wich one it is).

Your survival: that's an issue. Basically, you want time to regen after a tick of necrotic plague before infest. Keep in mind that infest will remove intervene. And that the shambling horror's shockwave will too, so avoid it (by staying 20-25 yards away from your pet).

For plagues 1, 2, 4 and 5, he will infest after the third tick, so you want to take the damage from the first tick, then chimera shot + intervene. You can mitigate damage with glyphed raptor strike if you can afford the loss of dps.
Plague 3: the difficult one. If you are a dwarf: stoneform on the second one, and for the second spawn of ghouls, feign death before he casts infest and delay it for 1-2 seconds (but not too long, or plague 4 will tick just as he infests), and intervene for the first two ticks of plague 3. If not: make sure you do not delay the infest (either by not feigning death, or doing it after he casts infest), and it should arrive before the second tick. Mitigate the first tick with either raptor strike or deterrence, or both and chimera shot right after. Then intervene after the infest and it should absorb for enough time to get another chimera shot past.
Plague 6: will infest after the second tick. So... very dangerous without stoneform. Best thing is to get him to phase 1.5 before he cast it.
So the last problem will be that: you must chimera as much as possible, feign death + misdirect, and losing about 3 seconds, dispel enrages, multi-shot...  And dps like hell. Guess who's going to have to manage his focus? Remeber: two steadies = about 55 focus with the passive regen and passive regen = about 6 focus/sec. So don't use arcane shot unless you're extremely high on focus (about 75+) or are above 50 and will do two steadies after it.
Probably the hardest phase, 1 error = 1 wipe, and focus management is capital for you and your pet to survive while burning down arthas's health.

One last thing: don't use your two rapid fires, or you won't have enough time for it to come off CD for the raging spirit.

Phase 1.5:
You will need a target raging spirit + petattack + charge macro.
He will run to the center. Put you pet on stay inside the platform. A raging spirit will spawn. Misdirect him to your pet and pop all cooldowns: he must die quickly. When the second spirit spawns, quickly finish the first if it's still alive then feign death. Make your pet build aggro on him.
If he becomes invisible, the only way to target him is with a macro. In that cast, better leave the pet on him for a while: if he isn't the nearest spirit, you will never be able to target him if both you and your pet stop targeting him. For the third, leave feign death and use deterrence. Make sure he melees you once, then send him on your pet. Once the ice collapses, multi-shot to get rid of the spheres on your pet, then kill any frost sphere aggroing you. Then quickly bandage and, after the infest, intervene if your health still isn't high enough. A healing potion can also be used.

Phase 2:
As long as two spirits are up, make sure your pet is well healed.
Tanking: you are a tank if you were melee'd a most 1 minute ago (in the video, the val'kyr aggro'd me 1 minutes 4 sec after the last hit). So you will want to be hit once every minute at least. To avoid damege (50K crit + infest = death), use intervene, taunt, then FD after the first hit (or dodge/miss/parry).
Beware: make sure you don't get soul reaper, and remember that after that he gets a haste buff, so don't taunt before he loses it.
If a Val'kyr still picks you up, then:
-if more than one try to pick you up at the same time, they get in an argument and fly away after giving you a good fright.
-if they try to take you one at a time, wait for the last, then wiggle your mouse while facing outwards to turn as soon as they let you go. Then disengage (macro'd with parachute) as soon as you turn. Sometimes works, but betting your life on it is a bad idea.
Mainly, dps as much as you can, taunt once in a while, and your pet should be in no danger.
The defiles are easy to deal with, and deal nearly no damage.
At 41%, take a last hit.

Phase 2.5:
Spirits will spawn faster. Dps the first, send the second one on your pet, kill the first, deterrence on the third and take a hit, then send him and the fourth on your pet. If the ice spheres get near you, feign death.


Phase 3:
At first, kill a spirit asap and use last stand to keep your pet alive.
For the vile spirits, use intervene once they aggro you, and try to take a hit in the last second or so. Finish the other spirits. Then all you have to do is intervene for the vile spirits + hit (you could get a hit every two intervenes, but it's risky) , and get him to 10% before he enrages.
If you are taken inside frostmourne: use aimed shot on the warden, get a hit from a vile spirit (they follow you, but keep aggro on your pet), then immediatly kill the warden before the lich king despawns.