At the start of the fight, quickly snipe Fyrus's forehead.
Grab either of the chains and try to walk directly away from Fyrus.
With the Master Sword, rollstab Fyrus's forehead. If fighting Fyrus with the Ordon Sword, do a jump attack + quickspin.
Stand to Fyrus's right side and aim an arrow at his forehead before he reignites. When his reignition animation is over, his forehead will have returned to the same spot it was in before the animation; shoot the arrow.
Repeat steps 2-4 until the fight is over (3 rollstabs total). With the Master Sword, rollstabbing is faster than targeting and pressing A for the fancy finishing move on the final cycle.
Pulling Fyrus' right foot to knock him down is slightly faster than pulling his left foot.
All the pots around the boss room alternate between heart drops and arrow drops. It is possible to obtain these drops without losing any time between rollstabbing Fyrus and his forehead becoming vulnerable to another arrow shot. This is recommended in cases where arrow count or health will be important after finishing the dungeon.