If you speak with a Caladrius demon, found more prolifically in Shinjuku's outer area than in the overworld, you may be able to activate the Challenge Quest "Cu Chulainn's Training", which can reward you with the Brionac weapon.
You will be challenged to find Setanta, a demon you can find north of Kasumigaseki in the Bugeikan, which is west of the guide in that region.
|31||Fairy||N/A||Physical, Light, Dark||Force (Repel)|
Offensively, this guy doesn't offer much. He is capable of raising the damage of his Physical/Gun attacks, convenient as one of his moves is a party-wide physical attack initally able to do around 80 damage at Level 25. Additionally, he has the extremely powerful Fatal Sword, likely to one-hit-kill you.
Finishing this guy quickly is the main goal here. Attacks that hit multiple times work well, so long as they are not of the elements mentioned in the above data box. Strategically, other than that, you don't have much to go on.
Winning this battle will net you the Brionac sword. It's not too great a weapon compared to the Tokkosho, although it does have a 50% chance of dealing three or four hits, which supercedes the Tokkosho in power. It also can hit multiple enemies. I'd probably just sell it, but it's up to you.