Battled him in NG+ just after fighting Owl in Ashina Castle. Tried countless time against Owl in Ashina (I had to relearn his moveset because deflecting does very little at this point, you have to be much more aggressive and he hits very hard). Surprisingly, Owl (Father) was easier to defeat, he somehow hits for less HP and has more openings. I'd recommend staying close to him all the time in a two-three slash combo then deflecting his counter and repeating, this action will often lure him to use the shoulder tackle + spark sword attack, you can get a free hit if you only step backwards during the animation where he throws the spark gunpowder and dash forward at the end of the slash animation. As long as you stay aggressive you can just connect hits everynow and then, drop his posture and catch him while he jump backwards and stagger everytime he fails his running slash, second phase only makes him have more openings.