The Moonlit Princess is a Side Quest in Tears of the Kingdom. Side Quests are small adventurers that players can partake in to earn a small reward for their efforts and immerse themselves in the lore of the game further.
Even though Side Quests rarely result in a meaningful reward, it is nonetheless rewarding to engage in them. The world of Hyrule would be bland and lifeless without the residents that make it home, and fulfilling some of their requests is the least we can do to appreciate their wondrous existence.
Starting The Moonlit Princess Quest
To start the Moonlit Princess side quest, you will first have to complete the Sidon of the Zora part of the Regional Phenomena questline and get clean water to the Zora by clearing the Water Temple. Once you've brought clean water to Zora's Domain, talk to Seggin, who is standing on a bridge that leads out of Zora's Domain to the west.
Seggin will tell Link about how he still yearns for the days when Princess Mipha was still alive and would very much like to see her wielding her signature trident in the moonlight one last time. There is no Mipha in Tears of the Kingdom, but there is a statue of her up at Mipha's Court.
To fulfill Seggin's request, you will have to take a picture of Mipha's Statue on a clear night filled with moonlight using your Camera.
Taking The Picture
Zora's Domain is often raining, so you might need to wait out rainy weather. The best spot to do this is at the Inn inside Zora's Domain. There is a fired-up cookpot you can use to wait out the rain and clouds.
Remember to select the Wait until Night option when you're waiting.
Once the weather clears up and you see the moon in the sky, head up to Mipha's Court by teleporting to the Ihen-a Shrine. Line up your Camera so that the moon is in the background and take Mipha's picture.
You should see a red exclamation mark signifying that all the conditions to fulfill Seggin's request have been met. If you don't see this mark, it means that something is missing. Either the night is not moonlit, or you don't have the moon fully in the frame. Wait for the moon to travel into the frame or reposition yourself. If you see a blood moon, wait it out and take a picture with a blue moon.
Return to Seggin and talk to him again to show him the fruit of your efforts. Seggin will accept the picture and reward you with a Zora's Sword, thus completing The Moonlit Princess side quest.