Puck the Elf mini-game:
Successfully complete the game under the easy difficulty setting. 

Battle arena mode:
Successfully complete the game under the normal difficulty setting. 

No limit mode:
Successfully complete the game under the very hard difficulty setting. 

Easy hard mode prizes:
Use the following trick when obtaining the hard mode prizes. Set the difficulty to easy
and proceed to the final stage save point (before fighting Balzac's first form). Quit and
save the game. Set the difficulty back to hard and continue the game. Even though you
completed most of the game under the easy difficulty setting, you will still get the
prizes for hard mode. You still have to complete the final stage in hard mode, but
some tough sections (such as the battle with Zod) are a lot easier.