From the Super Mario Wiki
100m Backstroke is an Aquatics Event that appears in the Nintendo 3DS version of Mario & Sonic at the London 2012 Olympic Games. The objective of the event is to swim the 100 metres in the fastest time. The starting World Record for this event is 0:51.94, and the starting Olympic one is 0:52:54.
100m Backstroke appears as the first challenge of Girls Episode 2 Peach in a Pinch in story mode, in which Peach must beat three Peach Fog Imposters. It also appears as the challenge of Girls Episode 3, The Mysterious Thief, where Peach must beat Rouge.
The event is played by drawing circles on the touch screen within the marker shown on the top screen. The player has two circles to practice, before completing the rest of the length at a slower speed. Once they reach the end, they will turn around and do the second length at a faster pace. Each circle will be given a percentage based on how much of the player's line was in the circle, with 90% or more being Perfect, 70% or more being Great, 40% or more being Good and anything under 40% being bad. The rating of the stroke affects the character's speed, with better ratings giving a greater speed boost. The speed that the final few strokes are performed at is decided by the rating of the last circle that the player drew.
1) Swim: Draw loops on the Touch Screen.