This request is given by Kagero the Merchant, who runs the market, after discovering the spot where Shrine Ruins Sub-camp 1 can be built.
|Kagero the Merchant||Slay 8 Izuchi in the Shrine Ruins||Shrine Ruins Sub-camp 1|
Where to Find Izuchi
The easiest way to complete this request is to accept the 1-star Village Quest, Help with Maintenance. Not only does that quest require killing 8 Izuchi, but all Izuchi will be marked on the map. Otherwise, try searching in areas 4, 8 and 12.