You’ll meet a lot of interesting characters during your adventure in Sekiro: Shadows Die Twice, but the assassin Tengu of Ashina is one of the most curious fighters. Found int he temple right after the serpent segment, speaking to him will trigger a mini-quest to hunt “Rats” somewhere in the world. Thankfully, they aren’t far and are fairly simple to kill.
You can find the rats in a large courtyard to the right of the Ashina Castle Gate. When you spawn in at the idol, kill the gunman and then hop onto the top of the gat. To your right is a large courtyard where the three rats are located. They will be in the back left corner digging in the dirt by the tree.
Equip the Loaded Axe and sneak up on one to initiate a stealth kill. After that, quickly lock on and attack the other small being with the axe. This will split it open and leave him exposed for a shinobi death blow. The last one will behind you and try to throw poison darts at the player. Block these, close the gap, and quickly dispatch him.
Now run back across the field you fought the horseback samurai on and speak to Tengu. He will reward the player with a new branch of skills and abilities that you can unlock. This mini-quest is very easy and is really worth completing since the reward is quite nice.