Taming Deth'tilac can only be accomplished when his health is below 20%.
Deth'tilac has a "Deth Strike" ability that instantly kills when it lands while taking 10% of his health. Your pet will die frequently. Using approximately eight of his Strikes will drop him to the needed 20% level for taming.
One of the best methods is to use your pet/[Snake Trap], plus [Concussive Shot] and [Ice Trap] to keep him at bay while kiting. Your pet and the snakes will receive his Deth Strikes, and for this reason you need to keep reviving your pet whenever you can. Eventually Deth'tilac's health will be sufficiently low for the tame. Dismiss your pet and do the tame at max distance with an Ice Trap between you and the spider.
Some suggest using a spider pet of your own during the encounter, as it's web ability will provide an additional slow against Deth'tilac.
An alternative to solely snake trap and pets is to also have a friend take the Strikes for you.