The Hunt Club is located in the Hunter’s Camp area of the Phon Coast. You cannot initiate the Hunt Club side quest until after you have completed the Draklor Laboratory and arrived at the Balfonheim Port for the first time.
Warp to the Phon Coast and look for a hut with a bunch of Bangaas standing in front of it on the southern shore. Speak to the Huntmaster up at the top of the stairs. He will tell you that he is looking for “birds of prey”, the best of the best! He will ask you if you are a “bird of prey”, select the correct answer and he will ask you to track down Thalassinon, a turtle located in the Phon Coast, and obtain the Shelled Trophy.
Exit the Hunter’s Camp to the east heading to the Vaddu Strand. Take the pathway up the side of the cliffs in the easternmost section of the Vaddu Strand and perch atop the edge of the strand looking down towards the shore. Thalassinon will spawn down on the shore if you wait there long enough.
Run down to Thalassinon when it appears. There is no particular strategy required in order to defeat the tortoise. Take it down and obtain the Shelled Trophy and head back to the Hunter’s Camp.
Speak to the Huntmaster again and he will tell you that you have passed the test and that you should speak to the three Bangaa brothers. The three brothers (Atak, Stok and Blok) are standing just below the Huntmaster.
The goal of the Hunt Club is to trade in trophies to either Atak, Stok or Blok, which will unlock different treasures that you can purchase from the Shifty-Eyed Man’s store. The treasures that unlock depend on which Bangaa you choose – Atak unlocks weapons, Blok unlocks armors and Stok unlocks items. You can obtain the weapons and armor that are unlocked through alternative means, so you should focus on turning in trophies to Stok.