Free Play:
Complete all Training missions to unlock Free Play for Arcade Mode.

Unlock Hunters Files:
Unlock the different Hunter's Files by doing the following:

Player Character Files - Finish Arcade Mode (multiple times)

Enemy Files - Kill/meet enemies (any mode except Training Mode).
Boss Files - Kill Bosses in all modes, including Training Mode.
Item Files - Buy/earn each item in Special mode.
Miscellaneous Files - Finish all missions in Special mode and complete Training Mode