Successfully complete one of the following tasks to unlock the corresponding art at Valeria's Shop:

Publicity Art 1: Win one tournament in the World Competition or play 1,500 battles.
Publicity Art 2: Win one league tournament in the World Competition or play 1,500 battles.
Publicity Art 3: Win the tournament in the World Competition three times consecutively or play 1,500 battles.
Special Art Group: Clear Chronicles Of The Sword mode or play 700 battles.
Special Art Special Group: Clear all missions on the Hard difficulty setting in Soul Arena mode and score a "Clear" or higher rank or play 800 battles.
Special Art V's Mansion: Clear Chronicle 17 in Chronicles Of The Sword mode and meet the bonus requirements or play 700 battles.