The Mysterious Thief
From the Super Mario Wiki
The Mysterious Thief (also referred to as Girls Episode 3 and Girls 3) is the third Girls episode in the Story Mode of the Nintendo 3DS version of Mario & Sonic at the London 2012 Olympic Games. The episode is unlocked after completing Peach in a Pinch, and unlocks Mario and Sonic once it and Enter Bowser?! are completed. This episode, along with the other Girls and Challengers episodes, must be completed to earn the Story Mode 2 badge, and its completion is also required to unlock the Story Mode Cleared badge.
Peach, Daisy, Amy, Blaze and the yellow and blue Toads follow the purple Toad through Hyde Park, where they encounter Rouge. Amy asks rouge what she is doing there, and rouge claims that she was just looking around, though the purple Toad accuses her of talking to the Peach and Blaze Fog Imposters. Blaze asks Rouge to explain, and she tells them that she intends to trap the real characters in the Phantasmal Fog and send the Fog Imposters to take their place. Rouge tells them that she will let them all out of the fog if they win an event against her, and Peach takes up the challenge.
Peach manages to beat Rouge, and Blaze then confronts her, asking her to explain. Rouge seems confused about how she got to Hyde Park and where she is, so the others explain what she said and ask her if she knows about the fog anyway. She reveals that someone instructed her to use the fog to trap them, and that there is a Fog machine in the park. She leads Peach, Daisy, Amy and Blaze to it, while Peach tells the Toads to wait where they are. Blaze attacks and destroys the machine, causing the fog to clear, allowing them to head to the Olympic Stadium, though they still want to know who caused the fog and asks Rouge if she remembers anything else. They are interrupted by Mario, Luigi and Toad, who came to see if they were alright, noticing that they have already cleared up the fog. Daisy and Amy explain what happened, but Rouge is unable to remember who told her to trap them in the fog. Toad suggests that it may have been Bowser, but this prompts Rouge to remember that it was Dr. Eggman at the British Museum. She explains that she was admiring the treasures when he arrived with the fog, she inhaled some of it and could not remember anything after that. Toad theorises that Bowser and Dr. Eggman have teamed up again, and decides that he should head to the British Museum with Mario and Luigi, and asks Rouge to stay behind with the girls.