Beat him five times in a row. I can't remember the exact locations, but just follow the path and check every nook and cranny and you should find all 5 of the battles. If the 4th battle you see takes place at the entrance, and after it the summoner runs away and Tidus slumps, you've missed one battle. But imo, unless you want to take Penance on, leave him (DY) alive, as he's a good source of Dark Matters and Ribbon equipment.