Tityus explained that the bounty hunters bet on who can hunt down the most Calydons each week--the winner last time was a Shugo named Nagrunerk. He promised you a reward to hunt some Calydons and let him take the credit. After you got rid of some Calydon Chasers and Calydon Shamans, he was pleased that he'd have enough kills to beat his Shugo opponent.