On each cycle, Armogohma begins with an RNG-determined timer lasting 200-300 frames. Until this timer runs out, it is guaranteed to continue crawling around the ceiling. Once the timer runs out, Armogohma has a 50% chance of opening its eye and shooting its laser at every light it reaches. If Link has fewer than 4 arrows when Armogohma would open its eye, then it will spawn eggs instead so that the player can get an arrow drop, then begin another cycle.
Shoot Armogohma when it opens the eye on its back. Shooting from near where it will land is ideal, but its crawling pattern is random, so tracking it with the bow from the center of the room is a good choice.
Use the Dominion Rod to smash Armogohma with the nearby statue. The statue's fist will miss Armogohma if swung before Armogohma has finished falling or if the Dominion Rod bonks on Armogohma's body or legs during the animation of Link swinging it.
Armogohma will now climb up a wall, onto the ceiling, across a light, and then towards the center of the room to drop the first round of eggs. Stand near where the eggs will drop so that it is possible to kill all of the small spiders very quickly after the cutscene ends. Standing in the middle of the egg drop can result in Link getting stun locked if holding L to raise the shield.
Repeat steps 1 and 2.
When Armogohma drops the second round of eggs, there is no cutscene. Stand beneath her and repeatedly spin attack to kill the eggs before they hatch.
Repeat steps 1 and 2 for the "final" hit.
It is fastest to bomb arrow the eye as it runs away, as it only takes one bomb arrow to end the fight. 3 normal arrows will also work, and the first arrow will stop the eye from moving, making the remaining 2 require no aim. The eye normally moves slightly to the right from Link's perspective once the cutscene ends, so prepare to aim slightly right.
This fight can vary in speed significantly due to RNG at multiple points: