To beat Beemer go beside a tree near the end and you will miss out on a hairpin.
On the race against Cosworth (The cosworth challenge!) there is a shortcut that takes a bout a second off Cosworth every lap. (the one he uses in the last lap if you're in front of him!) You have to get a good run into that corner and then you will (Hopefully!) drive right up the corner and jump into the cave! With a little bit of practice you should be able to do this in every lap.
On one of the Medium tracks go through the rainbow arch on in the cliffs after the first turn it skips out a little of the track.
To beat Tetsuo after beating the medium tournement - there is a short cut. Get to it by turning right into the bushes after the tunnel.
Race As Cosworth
Finish in first place in all races in the easy tournament. Then, defeat Cosworth at Millennium Park.
Race As Tetsuo
Finish in first place in all races in the medium tournament. Then, defeat Tetsuo at City One.
Race As Beamer
Finish in first place in all races in the hard tournament.
Full Turbo Bar
Hold the brakes and accelerate at the same time, do two 360s, then release brakes to get a full turbo bar.
Hold the brakes and accelerate at the same time. The kart should just stay in the same location. When the brakes are released the turbo will automatically activate.