To start this quest, talk to the Sea Hunter and choose Pursuit Of A Poacher. He will say the following:
Pursuit of a Poacher
You've done well so far in your tasks. Only a couple more to enter the highest ranks of the Sea Hunters and obtain access to the best of gear.
This time I want you to hunt down a poacher. These poachers are generally found on jungle islands. They usually carry with them an amulet. Bring me this amulet as proof of a job done.
Upon starting the quest, the Poacher's Amulet will have a chance to spawn on any Poachers encountered on Jungle Islands. It has a high drop rate so kill a few of them until it drops, then returns to any Sea Hunter to finish the quest, by choosing the same dialogue option. He will say the following once you finish the quest:
Deliver the amulet.
I see your quest went well! Very good then. You may access new gear. Talk to me when you are ready for your next task.