Highlight "Options" at the main menu, then hold L + X + Y, then press R. An option for the cheat menu will 
appear at the bottom of the screen

All cars:
Highlight the "All Cars" option at the cheat menu. Press A(2), Y(2), L(2). Hold R + X, release the buttons, 
then then hold L + A

Car collisions:
Highlight the "Car Collisions" option at the cheat menu. Hold L + R + X + Y + A, release the buttons, then 
press X, Y, A

Random battle mode weapons:
Highlight the "Random weapons" option at the cheat menu. Hold L + A and press X, Y, release the buttons, 
then hold R + A and press X, Y

Toggle demolition battle mode:
Highlight the "Demolition Battle" option at the cheat menu. Hold L + A, then press Y, X, release the buttons, 
then hold R + A, then press Y, X.

Invincibility:
Highlight the "Invincible" option at the cheat menu. Hold L + X and press Y, A, release the buttons, then 
hold R + A + X + Y.

Super tires:
Highlight the "Super Tires" option at the cheat menu. Hold R and press X(3)release the buttons, then hold 
L and press A(2), Y

Brakes:
Highlight the "Brakes" option at the cheat menu. Press Y(3),release the buttons, then hold L + R + A + X


Car mines:
Highlight the "Car Mines" option at the cheat menu. Hold L + R + X and press A, Y,release the buttons, then 
press A, Y


Cone mines:
Highlight the "Cone Mines" option at the cheat menu. Hold Y + R + L, release the buttons, then press X, then 
hold A + X, release the buttons, then press X.

All parts:
Highlight the "All Parts" option at the cheat menu. Hold X + Y + A + L + R, release the buttons, then hold 
Y + A. Release, then press X(2). 


Invisibility:
Highlight the "Invisible Car" option at the cheat menu. Hold L + X, release the buttons, then hold R + Y. 
Release the buttons, then press A. Hold L + R and press X. Release the buttons, then press Y(3). 

Invisible track:
Highlight the "Invisible Track" option at the cheat menu. Press R, L, Y, X, A(2), X, Y, release the buttons,  
hold L + R and press A.

All tracks:
Hight the "All Tracks" option at the cheat menu. Hold A + X and press R, release the buttons, hold X + Y and 
press L, release, press A(2), Y(2), then hold L + R and press X.

Track orientation:
Hightlight the "Track Orientation" option at the cheat menu. Hold L + R and press X, release the buttons, 
then quickly press A, X, Y. Hold L + R and press X.

Super speed:
Highligh the "Super speed" option at the cheat menu. Hold Y + R and press L, release the buttons, then hold 
A + X. Release the buttons, then press A(3).

Submitted by FiresmithB and an unknown person