Cheat Mode:
Press X + Z + Start at the options menu to unlock the "Password" selection. Passwords for various time attack tournaments may now be entered.

Ride a Dolphin:
Enter DLPHNMOD at the password screen to ride on the back of a dolphin in free run mode. You can still perform tricks on the dolphin, but you can only do backflips and barrel rolls.

Aquatic Autonomy:
Press the Left Analog-stick while a track loads to control the water.

Control Title Screen:
Press the Left Analog-stick when "Start" appears on the title screen to move it on the water.

Alternate Costumes:
Highlight a racer and press Z at the character selection screen.

In-Game Reset:
Hold X + B + Start during game play.

Cool Ocean Track:
Beat the game in championship mode while playing the normal difficulty setting.

Aqua Maze Track:
Beat the game in championship mode while playing the hard difficulty setting.

Victory Gate Track:
Beat the game in championship mode under the expert difficulty setting.

Weather:
Beat the Expert Championship in first, second, or third place to unlock the weather conditions in Time Trial mode under the expert, hard, or normal difficulties.

Try Mode:
Beat training mode under the beginner and master difficulty settings to unlock the "Try" option on the training menu.

No Patience:
For a quick start press A immediately before "Go" is announced and the light turns green.

Tsunami Zone:
Start the game in Free Roam and go to Dolphin Park. Go straight ahead and a little off to the left you should be able to see some buoys that represent the bounds. Quicly keep going towards the bouys and use turbo to make it there before the out of bounds timer gets you and you'll enter a round area where the waves are big enough to trick off.

Thanks to Revolution readers water-logged and CRG!