To unlock the Hydraulics Mini-Game, you have to win a Raceday in Career mode that has the Hydraulics game as an event.

When you get half way on a Raceday you will be asked to select from three random prizes. Choose on any of them to see what you get. You will be asked if you want to keep dominating or leave the raceday. Turn off the Nintendo DS then turn it back on again. Continue your career. You will be asked to select a prize. Repeat this as many times as desired.