Unlock all characters in Exhibition:
Go to Exhibition, then go to the character select screen. Hold L and press D-pad Left, White, D-Pad Right, White.

Max stats:
Go to Exhibition, then go to the character select screen. Hold R and press D-pad Left, White, D-Pad Right, White.

Big Head mode.
During play, hold L and quickly press B, A, B, Y. Repeat to disable.

Big Chests:
During play, hold L and quickly press B, Up, Up, B, Y. Repeat to disable.

Thanks to Revolution readers EJW, phonecaller and STW!