Complete the game and save. Now there will be an extra 'bonus' option in the main menu. Doing the following will unlock the following modes in that menu.

Boss Battles Mode:
Complete the monster encyclopaedia.

Gunvard Revival:
Destroy all the marked objects in the village.

Rabbit Battle Mode:
Beat the Raging Rabbit after completing the game.

Rival Battle Mode:
Complete the game.

Sound Test Mode:
Complete all weapons.

Summon Night 2 Battle Mode:
Get the highest Craftsmanship rank.