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This quest is triggered by speaking to Yukie at the front counter of the Chiki Mei-Mei noodle shop. Yukie knows that you are a vampire, but she doesn't seem to care. She'll tell you that she is a demon hunter and has come to slay a beast called a Hengeyokai. Apparently, the Hengeyokai killed her master, but she has been unable to track it down to carry out revenge. Yukie asks you to let her know if you come across it in your travels.
Leave the noodle shop and pay a visit to Ming Xiao at the Golden Temple. Ming Xiao knows about the Hengeyokai because he previously announced his presence in her domain. She'll reveal this his name is Zygaena and that the demon is currently entertaining clients at the Red Dragon restaurant. Getting this info nets you two points of Experience.
Exit the temple and proceed to the Red Dragon, where you'll find a man sitting at a table in the back of the bar. Speak to him to learn that Zygaena is a business associate of his, but one that he doesn't really care for. Offer to kill the Hengeyokai and the man will let you pose as him at a meeting being held at the local fish market. Successfully arranging the meeting gets you another two points of Experience.
Cross the street to the Chiki Mei-Mei noodle shop again and tell Yukie about your success. She's a little reluctant to let you join her in killing the Hengeyokai, but tells you to meet her at the Golden Oceans Fish Market. Go through the alleyways of Chinatown until you arrive at Zhao's Imports, then continue to the end of the block to find the fish market at the very end. As promised, Yukie awaits your arrival outside.
When you enter the fish market, you'll find that the man from the Red Dragon restaurant was indeed the demon and not just a business associate. He will proclaim victory in getting you both in one place and then transform into a large fish-like monstrosity. The Hengeyokai can bring you to Final Death quickly at close range, so use ranged weapons and disciplines while Yukie keeps him occupied with her katana. If you're having a tough time with the demon, lure it toward the tanks on the wall. If the demon strikes a tank, or you shoot it yourself, it will be showered with liquid nitrogen and frozen in place for several seconds (allowing you to hack or fire away at it with impunity). Be careful when doing this, however, since the same will happen to you or Yukie if you're hit. Once the demon falls, Yukie will bid you farewell and you'll receive three points of Experience.
If Yukie pulled out a Crossbow
during the battle (which she doesn't always do), you can kill her at the end of this quest and take it for your own. Other than the Hot Stripper Assassin Action!
and Ming Must Die!
quests, this is the only other place I know of to obtain the weapon. Additionally, before leaving the fish market, follow the center row of support pillars to the back of the warehouse. On the ground behind the last freestanding pillar is a money clip with $200.