DK tank is the best but it requires some good playing.
Unless you get unlucky with breaths you can tank it indefinitely without assistance, although a pet/priest rotation will help enormously.
First breath: Bone shield + avoidance trinkets you have them.
Second breath: if you used avoidance trinkets or lichborne, bone shield should still be up.
Third breath: Icebound fortitude
Fourth breath: Anti Magic Shell
Fifth breath: Bone shield, or if you dont have it yet, AMZ + fire prot potion.
But yeah once the first drake dies and the vesperon has landed, boss will go purple, at this time you need to stop auto attacking, keep up only frost fever if you can, you need to save GCD's.
Moment he loads a breath, right click him to hit him and lose the debuff, then quickly pop one of the cooldowns i listed above.
If you have no CD's left, be sure to communicate this to your priests/pallies/hunters (whoever can save you), and they should use something on you for the next breath.
Next patch however a blood death knight will be a great tank for sartharion, simply because of will of the necropolis. It will reduce breath damage by 15%, and you'll also get 15% reduction from frost presence, 4% from spellshattering on weapon, 2% from meta gem, 3% from blessing of Sanctuary, 3% from vigilance. Anti magic shell will have a lower cooldown, Vampiric blood will grant you 15% health for 30 seconds every minute (when glyphed). Most a breath will be able to hit for is around 35k if you can lose the debuff, so you should have enough reduction to get it to 28k without cooldowns, which is quite easy to get. You'll lose bone shield but its being nerfed anyway, Vampiric blood will cover you for 30 seconds, and for the other 30 you can use IBF and Anti magic shield.