First, talk to the Huntsman and he will say the following:
You've breezed through my requests so far with ease, but now I've got a final challenge. With my ankles in prime condition, I'm nearly ready to venture back out into the jungle. However there's a particular beast that sometimes appears in the jungles of these seas, devouring any who gets in his way. He is a rare and powerful tiger known by the locals as Luthor.
If you find Luthor in your travels, slay him. But be wary, he will be no easy foe. If you manage to kill him, cut off his tail and bring it back to me as proof. Once you do, I've got one last reward that I think you'll find of particular value.
You need to find Luthor, the king of tigers. Its a tiger, so it will appear only on jungle islands. If a tiger is already present on an island, Luthor will not spawn. Finding it can be pretty tedious and can sometimes requires the player to travel to a lot of jungle islands. If you have gold and find an Inn, remember to ask the Innkeeper for direction to the nearest jungle island.
Once you've finally found it, it's time to hunt! It's highly advised to be armed with damaging arrows (e.g. Hunter's Arrows, Poison Arrows and otherwise Hardstone Arrows) to do as much ranged damage as possible before engaging in melee combat. Strong Bandages and White Flower Potions are vital, but so is also dodging and blocking. The beast also behave like the Tiger in terms of running away when his health is under 25%. If he does, he will despawn if there's enough distance between him and the player.
When Luthor is defeated, it will drops the Luthor's Tail. Return it to the huntsman and he will say the following:
Give the tail.
You've done it! I must say I am surprised. Killing Luthor was no easy task. Anyways, as promised, here is your reward.