Location: Waford South
Petitioner: Madame Julie
Reward: Varies; see below
Objective Reward: Varies; see below
In order to unlock this chain of Side Stories you first need to complete the events of Alabasta and return to Waford. Once you do, speak to Adio on the west side of his hut to open the way to the Dust Ruins. Along the short path to the Dust Ruins and on your right is a hole that Chopper can enter. Inside the cave beyond is a door for Zoro to slice through, and on the other side is a Yoisa.
This Yoisa is called Madame Julie, and she's big on accessories. She decides to employ Robin in creating new accessories via fusion. Presenting Madame Julie with the results of Robin's work at campsite will earn you rewards. Activate the Yoisa Sign beside Madame Julie so you have a quick path back here each time.
This is a multi-part Side Story, so we'll separate it out into its individual quests below. Note that although you can begin this Side Story early in One Piece Odyssey, you can't complete every step of it until you reach Chapter 7.
Part 1
Madame Julie starts off simple, and wants Robin to fuse together a basic accessory with two abilities. Adding the powers of any grey accessory you have will do just fine. If you're lacking in accessories to fuse you can buy more from one of the Yoisa Shops in Alabasta. There's also one inside the entrance to the Dust Ruins, though you need to make a return trip to Alabasta before you can reach it.
Take the resulting accessory back to Madame Julie to receive three Gator Durians and 18,000 Berries. You can also complete the Objective for the first part of the Side Story to receive a Technique Resistance +15 Ring.
Part 2
Madame Julie next wants an accessory with three abilities. This requires fusing the accessory with two other accessories, something Robin can't do during her first visit to Madame Julie's little cave. In order to create an accessory with the abilities you need you must first complete the events of Water Seven (Chapter 4), then fully upgrade Robin's Fuse Skill once you're back in Waford.
Take the resulting accessory back to Madame Julie to receive five Shock Kabuto Meats and 24,000 Berries. You can also complete the Objective for the second part of the Side Story to receive a Critical Rate +17 Crown.
Part 3
Madame Julie becomes quite serious once you complete Part II, and she challenges Robin to a final showdown. The objective? Create an accessory with four abilities, duh. To do this you'll need to complete the events of Marineford (Chapter 6), then fully upgrade Robin's Fuse Skill once you're back in Waford. You'll need six Cube Fragments to sufficiently boost Robin's abilities.
Take the resulting accessory back to Madame Julie to receive Julie's Ring and 36,000 Berries. You can also complete the Objective for the third part of the Side Story to receive a TP Charge Rate +25 Crown. This will end the Side Story.