Over the Moon

First things first, you'll find Kujirai Momiji hanging out at the Inazuma Fishing Association. This spot is located northwest of Inazuma City. Head over there and chat with her. She's got something she wants to show you and will ask you to meet her at a beach on Kannazuka Island later that night.

Okay, so for this part, you need to make your way to Kannazuka Island. Once you're there, head north from the northern Tatarasuna waypoint. You'll need to glide north from the waypoint until you reach the objective marker. Kujirai specifically asked you to meet her at night, so make sure you adjust the in-game time to be between 19:00 and 22:00. Once the time is right, you'll trigger a cutscene.

During the scene, Kujirai will share some personal stories about her childhood and her dream of becoming a fisherman, inspired by her father. Since the Lunar Leviathan isn't around, she decides to write a wish, put it in a bottle, and toss it into the sea. She then asks you and Paimon to do the same.

After you've both sent your wishes out, Paimon will spot a bunch of glowing fish. Kujirai reveals these are called Moonfins and, in a moment of realization, declares that *these* are the Lunar Leviathan! She explains that this is what they saw years ago when they were stranded, the same night Jiawei almost gave up. To help you catch them, she gives you her special fishing rod, the Moonstringer, which was made specifically for catching the Lunar Leviathan. She tells you to go ahead and fish up all the Moonfins. Doing this will finish the quest and unlock the "Reeling in the Moonlight" challenge. After you complete that challenge, you'll have one more chat with Kujirai.