The Ghostly Tower
From the Super Mario Wiki
The Ghostly Tower (also referred to as Sonic Episode 2 and Sonic 2) is the second Sonic 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 Sonic Arrives, and unlocks the episode The Blocked Bridge upon its completion. This episode's completion is required to unlock the Story Mode Cleared badge.
The Boo arrives at the Tower of London, where King Boo approaches it and checks that it was keeping watch. Sonic and Tails arrive shortly afterwards and listen in to their conversation. The Boo tells King Boo that Sonic and Tails are there, and that the Phantasmal Fog created Fog Imposters of Mario and Luigi, prompting King Boo to mention that Bowser was right. He asks the Boo if anyone saw him, and he claims that no one did as Sonic and Tails were the only ones there, and also explains that the Fog Imposters disappeared after losing to Sonic and Tails, angering King Boo. This causes him to believe that Sonic is as strong as Mario, which the Boo doubts. King Boo asks him to tell him if Sonic shows up, claiming he'll defeat him like Mario, which the Boo doubts before pointing out that Sonic and Tails are stood right behind King Boo. Tails demands the truth about the fog from King Boo, while the Boo suggests that they could defeat them or convince Sonic and Tails to join them. The Boos challenge Sonic and Tails to Badminton Doubles, which, although confused, they accept.
After their defeat, King Boo blames the Boo for their loss, before they both run away, followed by Sonic and Tails. Sonic and Tails lose the Boos, but instead find a Fog machine, which Sonic destroys with a Spin Dash. Tails is upset by this, as he wanted to see what made it work, until he notices that the fog has cleared up, and after realising the fog was what created the Fog Imposters of Mario and Luigi, he agrees with Sonic destroying the machine. Noticing that it is getting late, Tails suggests that they should head off so that they don't sleep through the opening ceremony the next day.