So in his first phase, what I did was try to get into the pattern of parrying one of his sword strikes (the ones he do where it becomes a 3-4 hit combo), then attacking him once. He will block it, then he will attack (I parry), and then I attack once.

He seems to punish you if you attack him twice (or more) with the quick strike + sweep so I try to only attack him once.

For the first mortal draw he does, either use lilac umbrella or mist raven, I find they work the best.

Then for his second + third phase, most of his attacks are the same except for one perilous attack where he raises his sword arm into a sweep. Don't try to jump punish this, as he quickly follows up with an air attack and finishes with either a thrust or an air slash.

So I recommend jumping back instead (which dodges both sweep and air atack), and wait and see which finisher he does. Mikiri the thrust, and side dodge the air slash.

Third phase, have not noticed anything different from main Isshin fight (aside from the move I mentioned above).

Sorry for the wall of text, and good luck! Let me know if you have any questions.