Question: what to do after you beat team aqua hideout in emerald?
Answer: Pyre and Route 122/Route 123/Route 124 and Route 125/Shoal Cave. Heal your Pokemon at the Pokemon Center, and you'll find your rival in front of the Lilycove Department Store behind the Pokemon Center. After beating her, go to the Lilycove Museum, and talk to the old man blocking the staircase.