To unlock the option to play any chapter at any time, complete the game once through and save your game after the ending sequence.

To unlock a New Game+ option, which will allow you to replay the game after you've beat it once with many of your items, skills (and more) already obtained, beat the game once through and save your game after beating the game. Then, start a new game using your old save file.

There's an unlockable, secret ending sequence that can be unlocked. To do so, collect each and every Secret Report in the game.