To access the following cheats, go to Extras, then Cheats, then…

Unlimited Shields:
Enter Triangle, Triangle, Square, Square, Square.  

Unlock Animal Ships: 
Enter Triangle, Circle, Circle, Triangle, X. 

Unlock Retro Ships:
Enter X, Circle, Triangle, Square, X. 

Unlock All Features: 
Enter X, Triangle, Circle, Triangle, Circle. 

Unlimited Ammo:
Enter Triangle, Circle, X, Circle, Square. 

Super Fast Ships:
Enter Square, X, X, X, Triangle

Mini Ships:
Enter Circle, Square, Square, X, Circle

Infinite Cannons:
Enter Circle, X, Triangle, Circle, Triangle

   

Thanks to Revolution readers Jehuty and Des!