The Greater Hunter is a quest accepted from Brave Sir Robin. The area marked on the map is the first time you encounter Bellegar. THIS IS NOT where he summons the demon. Instead, go to the area east of that near the labels "Ambush" and "Eugene". There you will find Bellegar again in a similar temple and there he will summon the demon. 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.