Be Arcia:
Beat the game using Normal Difficulty

Get Hard Difficulty Level:
Beat the game using Normal Difficulty

Get Super Hard Difficulty Level:
Beat the game using Hard Difficulty

Unlock "Liv Special PV", "Total Results" and "Extra Menu" options:
Beat the game using any Difficulty level

Play Previously Played Levels:
On stage 9 beat the boss and you will get the Map Selector which allows you to go to any completed level

Change Enemies on Previously Played Levels:
Beat the boss on level 10 to unlock Change Appearance which changes enemies on replayed levels

Destroy the final summon:
Slash twice then us the upper cut then summon up the 2nd summon monster it will die!