The Greater Hunter is a quest accepted from Brave Sir Robin. You need to go to the area marked on the map. Once there you need to kill the level 9 demon that Bellegar summons and take its claw. This demon will spawn from a random Bellegar Arena you visit. But this claw can also be gained from killing the Hellgate Demon which is the last of the 4 waves at the Hellgate.
When you return to Brave Sir Robin you will receive a default reward of 1500 exp, 320 gold, and a pair of magical gauntlets, as well as a choice from either 320 more gold or a random rare item.
Afterwards, the demon claw will be hanging on the boar trophy in the Rivertown Tavern.