The second part of the peace with barbarian quest - simply choose to fight the leader. Kontu will pay you anyway.

But you won't be able to trade Kanatos head with him. His shield is really good in that point of game.

I completed the first quest with the barbarian and took the second, but did not complete it. In the meantime, I obtained Kanatos' head, but couldn't sell it to the barbarian, only the second quest options appeared. What gives? Should you first sell the head and only then take the 2nd quest?

EDIT: I decided to fail the second quest in order to be able to sell the head and get the good barbarian shield. Much better than the pathetic 100-something experience and 1700 gold you get.