1. Try to stay in the middle. His combo that ends with him throwing sparks necessitates backing away, and if he's backed you up to a wall with it (and he will), that's bad. When that one ends, you can hit him with a throwing star if you want, and he won't block it.
2. Don't run away, he'll just chase you. Stay a medium distance from him so you can see his attacks coming, and you'll have plenty of time to use healing if you need to.
3. Keep your health up, so you can keep your posture damage low. Always lower it back to zero when he gives you breathing room.
4. Patience patience patience. It takes a long time to damage him enough, but once you have his stuff down, you're not in much danger, so don't rush.
5. Learn his attacks, of course. It seems like he has a lot, but he doesn't really. Let him attack, just parry or block and wait for the openings.
The places you can hit him are:
If he's standing still, you can walk right up and get in one hit, if your distance is just right to clip his right foot. Any closer and he'll block.
After his overhead leaping swing - dodge right (left dodge can catch you in that extended hitbox I mentioned) and then hit him.
After leaping over his perilous attack. If he's right on you, it's always a sweep, so jump, and hit him while you're in the air.
After that, he's very likely to do his "stand still with sword overhead" stance. DO NOT DODGE, or he'll change the attack. Stand still, right in front of him, and hit him once. When he grunts (in Japanese, it sounds a bit like "look out!"), then dodge to the side and get in another hit. You can even get in 2 hits, if you're bold - this move has a smaller hitbox than it should, so you can dodge quite late and be okay.
If he's further from you and does a perilous attack, especially after fireworks, it's always a long-range thrust. Immediately spam dodge without pressing a direction, and you'll get him in a Mikiri Counter, and can follow up with a hit.
In phase 2, all the same except, when he does his flaming bird thing (the bird lands on his arm, that's your sign), run as far away as you can and also maybe hide behind a pillar. Distance is more important, though. Keep out of range of the bird and the follow-up lunge.
The other bird move is when he disappears. Just run around and make sure he doesn't re-appear on top of you (he appears where the bird stops). Watch the range; his re-appear strike is longer than it looks. Once he does it, if you're close enough, you can get in a hit.
Here's a youtube video of someone who more or less fights him like I did.