Once you reach Ashina Castle for the first time, head around the back to where you’ll come across the Old Grave Idol. Peer over the wall and you’ll see a house with a hole in it, drop into this to meet with Blackhat Badger for the first time. Purchase the Loaded Umbrella from him along with anything else you may need and then continue on your journey.
Once you’ve reached Ashina Castle a second time after Mibu Village and Sunken Valley, return to the Senpou Temple area. Start heading up the path and you’ll spot him on the right, looking out to the kite.
Once he offers no new information, head down the path and use the Puppeteer Ninjutsu on the Rat to extend the kite. Return to Blackhat again and continue talking to him until he has nothing new left to say.
Sunken Valley Cavern
Travel now to the Sunken Valley Cavern Idol and you’ll come across Blackhat again, speak to him once again until he offers nothing new to say.
Ashina Castle - Final Visit
When you return to Ashina Castle during the Central Forces attack in the closing stages of the game, return to the Old Grave Idol. Drop down to the bottom of the area where you’ll find a watchtower and you’ll find Blackhat nearby, speak to him until he offers nothing new to say. Rest at the Idol and return to this location one final time, you’ll find a Mibu Pilgrimage Balloon on his body and conclude the quest.