1) Shoot Armhogohma when she opens the eye on her back, standing nearer is desirable as you will be able to get to the statue to smash her sooner. Doing a roll or two towards to the middle or the light she is heading towards while she moving can save a little time.
2) Smash Armogohma with statue, it is possible for the hammer to phase through her if you attack too soon after she has landed.
3) Armogohma will now climb onto the ceilling towards the center to drop the first round of eggs, due to the cutscene the eggs will hatch before you can kill them. Due to this, it is recommended to stand slightly away from the center of the dropping spiders so you don't keep getting damaged trying to spin attack if you were standing in the middle.
4) Repeat step 1 and 2.
5) This time the cutscene is gone so go directly where the eggs are falling and spin attack to kill them before they hatch
6) Repeat step 1 and 2 for the "final" hit.
7) It is faster to bomb-arrow the eye as it runs away, arrows also work but will require 3 shots (the first arrow will keep the eye in place for 3 quick shots). The eye normally goes forward to the right to where Link is facing, therefore be prepared to aim slightly right.
This fight can vary in speed significantly due to randomness at multiple points.
The number of lights she will move between every cycle is random, the minimum being around 3 or 4, furthermore movement between two adjacent lights is faster than movement between two diagonal lights, a 4-light pattern going back and forth adjacently is much faster than going back and forth diagonally. Targetting something (a spider or statue) does not influenced the number of lights you get.
After dealing damage to Armogohma with the statue, she will climb back to the roof. She normally walks over to one of the further walls, however sometimes she will climb up the nearby wall which is much faster.