A quick guide for the jumping mechanic from Jerry. Jumping is much faster than walking, so you should do it as often as possible. There are 2 different jumps, the short and the high jump. Jerry will do a short jump if you press/hold A for 1 - 9 Frames. For everything above it will result in a high jump. The height depends on how many frames you hold the A button.

At least, you will have to switch between short, middle high and high jumps in the game to receive ultimate speed.