Talk to Centurion Kishale in the Northern Checkpoint to begin this quest.
Getting Some Answers
There is one who knows much of ghilliedhus. Dulari, researcher and friend. As you travel to his campsite to the south, collect samples from those you fight. Attack from the sides or behind, but keep moving. An angered ghilliedhu is nothing to trifle with.
She also warns you that Guhilliedhus turn red when enraged, so watch out.
Your first priority is to hunt ghilliedhus and collect ghiilliedhu claws. You need to collect 5 of those claws, the quest tracker will keep track of how many you have gathered.
The Ghilliedhus are just a bit south, in the timeless woods. Kill them for their claws. Drop rates for the claws are 100%, so after you have killed five Ghilliedhus you should have five claws in your possession. Also, the claws are picked up automatically, but still be sure to pick up any other loot they might drop including items and gold.
After you get all five Ghilliedhus claws, your task is to take the claws to Dulari at his camp. The small camp is just a little south, down the road. Talk to Researcher Dulari. He saw you had to defend yourself along the path. Odd behavior from such normally docile creatures. Ghilliedhus are protector spirits, not soldiers. Researcher Dulari needs answers, and samples, as to what's going on.
Complete the quest and claim your reward.