In the first phase of this battle, stay on the ground close to the boss so you can run forward and avoid the jump attack (you don't even need to dodge roll).
The key to this fight is to pay very close attention to the hit box on the long-range scythe attack. You can avoid it entirely without even dodging, and many of the attacks can be negated just by staying slightly to the left or right of the boss.
Although it seems counter-intuitive, it's better to stay close to the boss and use sword attacks that let you jump up and slam down for much of the first half of this fight.
During the battle, listen for the sound of the Phoenix just a second before he swoops by and sets the area on fire. When this happens, run underneath a platform and get ready for the boss to start throwing fireballs, which can be blocked with your shield or jumped over.
The second half of the fight plays out much like the first, except the boss will occasionally split into two. During this segment, stay far away from the blue version that has a long range attack, and keep up your normal strikes on the ground against the red version.