Provided you completed We Loved Once and True back in Chapter 2, you’ll receive another letter from Mary in Arthur’s room during Chapter 4. Read it and then make your way back to Saint Denis to meet her at the hotel.
You’ll need to keep a safe distance from her father as you trail him across the Saint Denis streets, make good use of the radar to keep track of which direction he goes. Eventually, he’ll reach his destination and sell Mary’s brooch and Arthur, being the dashing gentleman that he is, rushes off to get it back.
Head through the door in front of you to reach the street and then mount one of the nearby horses. Use a Horse Stimulant and then gallop as fast as you can after the wagon, if all goes well you should pull up to the side of the wagon by the time you head onto the second bridge. Press the [Square]/[X] button to jump to the wagon and then move toward the drivers to throw them off and take control of the wagon.
Quickly drive the wagon as fast as you can along the path and then across the water to the secluded spot. Beat Ashton a few times when you get the choice to get back the brooch for free and then board the wagon to return to Mary. When you’re given the option to go to the theater with Mary, take her up on the offer (for the Gold Medal) and sit through to the end (three acts) before leaving and completing the mission.