From the Super Mario Wiki
Dream Trampoline is a Dream Event that appears exclusively in Mario & Sonic at the London 2012 Olympic Games. It is set in Crazy Gadget from Sonic Adventure 2. The objective is to earn as many points as possible. The starting Olympic Record is held by Vector at 300 points.
In this event, players take turns in a one-on-one Round Robin style for doing tricks. To do tricks, players need to do what the action on top icon says, with four other icons as upcoming actions. At the end, if one player has done more tricks then the other, they earn a Victory Bonus worth an additional double of the number of tricks done in that turn while the loser doesn't get anything. But if it is a tie, both players earn a Tie Bonus worth the number of tricks done in that turn. If the player is no tricking, they can earn points by swinging the Wii Remote when there is a circle over the character. Depending on the timing, players earns one to three points. After all four players have tricked, the platform rises each time. After the third and final rising, the player's placement determines who goes against each other. The first two to trick are third and fourth place, and the second two are first and second. After first and second are done tricking, the event ends and players get their final placements.
The Aerial Dancer challenge is achieved by preforming moves with ten or more spins a number of times in this event. The criteria for unlocking each achievement are as follows:
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