The first half of this fight is very similar to the original battle, except the Owlking sends out three waves of glowing orbs instead of just one. Rather than wasting the stamina dodging all three waves, just dodge roll behind the boss when he starts his vertical black portal.
The second half of this fight is where things gets truly challenging. The orbs that land on the ground from the horizontal portal now permanently remain on the screen. This means you are going to rapidly run out of room to dodge.
To minimize the loss of ground, try to stay in the same left or right corner instead of battling in the middle. By keeping to one spot, fewer parts of the room will get covered in orbs.
If you mess up and the middle of the area gets covered, don't try to dodge roll through the stationary orbs. Instead, jump and attack at the height of your trajectory to hover and increase your jump distance.
Save your arrows for this second half of the battle so you have a damage dealing option when stuck on the other side of the screen.
Inevitably, you are going to get stuck in a position where the Owlking is on one side of you and the wall is on the other. The hit boxes for damage are his arm/wings and feet however, not his main body. If you dodge roll left and right quickly, you can still avoid taking damage when he strikes.