Location: Dressrosa City Area
Petitioner: Ribbon Searcher Dahlia
Reward: Toy Ring, three Nami's Cube Fragments, 500 Berries
Objective Reward: Perfected Exhaust Ball Plus
In order to trigger this Side Story you must first complete the events surrounding Dressrosa and leave for Waford. Once you come back, during Chapter 9, you'll find a bunch of Side Stories unlocked. This particular quest is located on the far west side of Dressrosa, on the west side of the Coliseum. The petitioner is a little girl, and she's standing on the side of the road.
The girl, Dahlia, has lost her ribbon. She believes that the Tontatta, a tribe of pint-sized fairies who live beneath Dressrosa, are responsible. Tontatta are known for living in plant-filled areas, using flower beds for transportation, and Robin suggests checking some nearby bushes for the culprit.
A few feet away from Dahlia is a small yard with some foliage sticking up over the stone wall. There's a Tontatta inside the foliage, and it promises to learn more about the ribbon. It also suggests looking around the fountain to the north. You'll find it northwest of the entrance to the Coliseum.
There are a few witnesses in this general area who can point you in the correct direction - including a Tontatta in the back of a wagon, near the entrance to the Coliseum - though the fairy you want is in a flower pot between two benches, near the bookstore in the northwest. The Tontatta will hand over the Keepsake Ribbon, which you can return to Dahlia for your reward. Piece of cake.