The drakotas stay rooted in place at all times. At the beginning of the fight the nameds are immune to damage and can be mainly ignored.
After you start the fight a group of adds will spawn, these come in fire and ice flavors. Kill all the adds keeping the ice-forged behemoth or heat-forged behemoth add as the last mob.
After the Behemoth dies he'll drop either a fire or an ice crystal depending on heat/ice on the floor.
The person who clicks it has the opportunity to hurt the drakotas of the opposing element. Kigara can be hurt by the person who picked up the ice crystal and Kelena by the person who picked up the fire crystal. Since I duoed this I'm unclear on wether the other group/raid members can hurt the drakota too.