From the Super Mario Wiki
100m Breaststroke is an Event that exclusively appears in the Nintendo 3DS version of Mario & Sonic at the London 2012 Olympic Games as part of the Aquatics category. While it has the same goal as the event it is based on of completing the swim in the fastest time, in the game the main focus of the event is on the breathing. It has a starting Olympic Record of 0:58.91 and World Record of 0:58.58.
In the story mode, 100m Breaststroke appears as part of the first challenge in Waluigi's Ambition, along with 1000m Kayak (Singles) and Handball, where Waluigi must beat Metal Sonic. It also appears as the first challenge for the first Tricksters bonus episode Dr. Eggman's Robots, where Metal Sonic must beat Waluigi, and as the first part of the second Tricksters bonus episode An Old Urn's challenge, along with Handball and Badminton (Singles), where Metal Sonic must beat Wario.
While this event has the same objective as the real life event it is based on, the game version mainly focuses on the breathing and uses this as the main way to gain speed in the event. The event starts 30 seconds in on the final length, with the character swimming at a constant speed. When the character's head comes up out of the water to breathe, the player must blow into the microphone. Blowing with good timing will give the character a speed boost, which will last longer if the player blows with perfect timing, but failing to blow will not give the character any speed boost. Partway through the event, the character's breathing speed increases, meaning that the player is able to gain more speed boosts. For the final stretch, the player has to blow for a long period of time to power their character through the water, with the speed dependent on how hard the player blows. If the player does not blow into the microphone the character will continue to travel at the same speed as before the final stretch.
Blow when the head comes up!