Sekiro - Tengu of Ashina And The Rat Hunting Quest
Tengu of Ashina is one of the many mysterious figures you can meet in Sekiro: Shadows Die Twice. You first meet him at the Ashina Castle Gate Fortress, shortly after you fight Gyoubu Oniwa. Tengu is a large, imposing figure, and when you first speak to him, he will ask for your help with his quest. If you agree, he will offer to fight by your side.
Rat Hunting Quest
Tengu is trying to track down and kill, Rats from the Senpou Temple. He will give you an item called Rat Description. The Rats are tiny little creatures and wear bamboo hats, making them easy to identify. You need to kill three of them to appease Tengu. They are also skilled assassins, so be wary when fighting them.
Rat Location #1
The first Rat is located right beside the Ashina Castle Gate Fortress Idol. Just turn around, and you will see him behind a rock. Be careful fighting him; they are treacherous little foes and will use poison attacks on you.
Rat Location #2
The rest of the Rats can be found by going to the Ashina Castle Idol. Go up the stairs in front of you and grapple on top of the closed gate. Now, turn to the right, and you will be able to see them under a tree. It will be possible to eavesdrop on them, so do this before you kill them.
Once all the Rats are dead, return to Tengu, and he will give you the Ashina Esoteric Text. This text will open up a new skill tree for you. Tengu is not quite finished with you yet, however.
Later in the game, you can return to the Castle Fortress and discover a note left by Tengu. It advises you that he has gone to the entrance of the Sunken Valley and that you can find him there. He is at the Great Serpent Shrine, and you can Travel straight there if you have already found the Idol.
Tengu will be there, talk to him and he will ask you if you have learned any new tricks. As long as you have access to the final skill in one of your skill trees, he will be impressed by your prowess and will give you the Mushin Esoteric Text.
Now, there are lots of interesting storyline clues about who exactly Tengu is, but I don't want to spoil them for you here! This guide is just about the Rat Hunting Quest, after all!