Recommended Level: 8
In order to unlock the first chapter of Agnea and Hikari's joint chapter you first need to complete the second chapter of their respective stories. For Agnea this means traveling to New Delsta, a city on the eastern continent that's closer to Cropdale than it looks. Hop on a boat at the anchorage to the east of Cropdale, then head south from the New Delsta Flats. Hikari's route is longer, requiring him to travel from Ryu, in Hinouema, to Montwise, in the far east of the Crestlands.
Once you've unlocked the chapter you can activate it by traveling to Ryu, where Hikari began his journey into the wider world. Place both Agnea and Hikari in the party to begin the story right away, or speak to the Tavern Keeper in Sai to trigger the chapter.
Agnea and Hikari will arrive in Ryu in time to hear a musician playing his lute by the fire. Agnea is enchanted by the sound, and the musician, Yomi, proves rather... pompous about her skill. She demands coin for a song. Bribe Yomi 800 leaves to hear her play... or to receive promise of a song the next evening. Yomi needs prep time.
Change the time to day, then back to night. Yomi is waiting, but, dangit, one of her lute strings has snapped. She needs some horse hairs. Have Agnea Entreat the nearby Stubborn Horse Owner for some Horse Tail Hair, then give it to Yomi. She's ready to play... er, tomorrow.
Switch from night to day to night again. Yomi's nowhere to be seen near the campire, but she's still in Ryu. Hop onto a canoe in the southern pond and ride south to the nearest dock. There's a rise here, and Yomi will be at the top. She'll play her melancholy song for Agnea and Hikari, then leave with barely another word. Chapter complete... though the story can't be finished until you finish up Hikari's main story.