EX-skills and forms
This is unlocked after clearing the game once. To play hard mode, press and hold the L button when you select "NEW GAME" at the title screen. In Hard Mode, Zero's weapons cannot be upgraded; therefore, chips can only be used with the Shield Boomerang, which is the only weapon that requires no upgrades to use a fully-charged attack from the moment you are given it. Moreover, Zero cannot obtain EX-skills and Forms, giving him no edge in battle. Any more bad news? Yes: the only form available in this mode is not the Normal one, but the Proto Form, that has low defense, i.e. Zero suffers double damage. This means that most bosses can defeat Zero in just two hits, unless he uses Cyber-Elves and/or Sub-Tanks. Anyway, since EX-skills are not available, there is no serious drawback for getting low mission score. The only thing it will do is prevent bosses from using EX-Skills, should you dip below an A-Rank.
After clearing Hard Mode
There is a prize if you clear Hard Mode. As the screen will tell you, save your game, then press L and Select when starting a new game to unlock the Gallery.