The Beaver Races are two sub-games in The Legend of Zelda: Majora's Mask.
The record holder for both races is Pier-Yves Lemire with times of 40.57 and 34.70.
Beaver Race 1
The strategy in the beaver race is to jump out of the water as often as you can as this is actually faster then just swimming through the rings. So it's just about planning the angle you'll get after coming out of the water so that you have the straightest line to the next ring and that you don't actually bump the ring with your head or jump over or aside of it.
Beaver Race 2
The strategy is the same as the first day except that this time you'll be able to get out of the water a lot less often because the rings are closer together. So it's more about keeping your path as straight as possible between the rings.