Battle Bosses Again:
After you've beaten the Almighty, save your game and then load it. Where the bosses were, there is now a black crystal to open and you can fight the bosses again.
Fight Piu Piu and unlock new title screen:
After you've beaten the Qualia with each pair of fighter, save your game and then load any of your saves. Talk to Piu Piu and answer yes, your battle with the legendary scientist will then commence. Defeat him with all characters and your new title screen will be unlocked.
After you've finished the game any new games you start will retain all stats, items and money,
Unlock Playable character Ayuta/Mana & Olgar/Vhati:
Beat the game first. Then, load your beaten game and a new map will be open. Go through it, defeat the Almighty and then save at the end. When you turn it back on your character select screen will feature arrows at the bottom to switch between the characters.