Taming Karkin is best done as a Marksmanship hunter. Use [Tame Beast] to get his attention, then use [Silencing Shot] to interrupt his Fieroclast Barrage. Use Tame Beast to finish it off.
For those not willing to spec into MM, do everything to maximize your haste. The Barrage has a five-second cast, so dropping your cast time of Tame Beast below that is obviously ideal, as the Barrage will not only hit you for a great deal of damage (meaning you'll easily die with the next hit), but it also interrupts your taming.