When he spawns on the ground he does a melee attack right? you can jump and parry that while walking towards where he spawned then hit him again when he jumps. I also noticed that when he spawns in the air and dash down you sometimes miss your nail strike, so i recommend staying still and jump then do a down strike, and delay your double jump so the fire disappears, or you dash to where he goes as a prediction and pull of another nail strike. Regardless of those, this run is really good.
To be honest I dislike nightmare king grimm. I mean I see the black giant skeleton with sword and crown when hear "nightmare king", but not a some random guy with strange hat or smth and who to be honest looks like woman