After you activate the four batteries in the Lightning Temple and activate the platform in the Room of Ascension, you must defeat Queen Gibdo.
Defeat Queen Gibdo in the Lightning Temple
Queen Gibdo has some of the same attacks, such as spitting a beam of sand at you, charging toward you, or flying toward you with her claws out.
As before, try to have Riju create lightning, then hit Queen Gibdo when she is within the lightning circle.
Hit Queen Gibdo with a lightning attack to turn her white. She will fly a short distance away and then fall onto the ground. Don't get close to her at this point, because she will lean back and create whirlwinds to knock you and Riju down. If a whirlwind hits Riju when she is creating a lightning circle, the lightning will disappear, so wait for the whirlwinds to pass, then talk to Riju to create a lightning circle, and hit Queen Gibdo with a lightning attack. Queen Gibdo is more vulnerable to the lightning attacks after you turn her white, so she will be temporarily stunned by the second attack, allowing you to hit her repeatedly.
Queen Gibdo is easier to hit when she stands still while preparing an attack, because at other times, she will walk from side to side, making it harder to aim.
When Queen Gibdo's health reaches about 50%, she will make the Gibdo hives generate Gibdos. Remember that you can only destroy a hive when its core starts to glow brightly. Talk to Riju to have her create lightning as often as possible, and try to destroy the hives while also dodging Queen Gibdo's attacks.
When you destroy a hive, a beam of light will shine down at that location. Lure the Gibdos into the light and they will turn white, making them vulnerable to normal attacks.
Destroy all of the hives as soon as possible, using the beams of light to help you destroy the Gibdos.
Continue to attack Queen Gibdo with the usual strategy until she is defeated.
After the Battle
There is a Heart Container for you to take after the battle. Talk to Riju and there will be a cutscene.
Afterward, you will be back in Gerudo Town. This completes the quest.
If you have done the quest Impa and the Geoglyphs and started The Dragon's Tears, you will find Impa and Cado nearby. They can tell you more about Geoglyphs that you haven't found yet. Read The Dragon's Tears for more information.
You can also return to Lookout Landing, where you might find some clues about where to go next for the Regional Phenomena quests. See the following links for more information:
While in Lookout Landing, if you have completed Camera Work in the Depths but you haven't started A Mystery in the Depths, you can talk to Josha, and she gives you some Giant Brightbloom Seeds and arrows. This starts the quest A Mystery in the Depths.
Also in Lookout Landing, if you have completed at least two Temples, you can talk to Karson to start the side quest The Incomplete Stable. There is a plank next to Karson that fits perfectly, so use Ultrahand to put it in the gap in the stable roof to complete the quest. After that, you can talk to Lester to use the stable services.
After Regional Phenomena
If you have completed all four Regional Phenomena quests, go to Lookout Landing and climb the ladders to get onto the roof of Purah's lab. Talk to her there, and there will be a cutscene. This completes the Regional Phenomena quest. Your goal now is to enter Hyrule Castle.