You have to complete one of the following tasks to unlock the corresponding Soul Arena mission:
Beloved (Easy): beat Amy in Tales Of Souls mode
Beloved (Normal): get a "Clear" or higher rank in Beloved (Easy)
Beloved (Hard): get a "Clear" or higher rank in Beloved (Normal)
Blast Chase (Normal): get a "Clear" or higher rank in Blast Chase (Easy)
Blast Chase (Hard): get a "Clear" or higher rank in Blast Chase (Normal)
Coin Collector (Normal): get a "Clear" or higher rank in Coin Collector (Easy)
Coin Collector (Hard): get a "Clear" or higher rank in Coin Collector (Normal)
Dancing Statue (Easy): get a "Clear" or higher rank in in Soul Smash (Easy)
Dancing Statue (Normal): get a "Clear" or higher rank in Dancing Statue (Easy)
Dancing Statue (Hard): get a "Clear" or higher rank in in Dancing Statue (Normal)
Hard Workers (Easy): Purchase from the shop.
Hard Workers (Normal): get a "Clear" or higher rank in Hard Workers (Easy)
Hard Workers (Hard): get a "Clear" or higher rank in Hard Workers (Normal)
Soul Smash (Normal): get a "Clear" or higher rank in Soul Smash (Easy)
Soul Smash (Hard): get a Clear of higheer in Soul Smash (Normal)
Sudden Death Rally (Easy): get a "Clear" or higher rank in Turntable (Easy)
Sudden Death Rally (Normal): get a "Clear" or higher rank in Sudden Death Rally (Easy)
Sudden Death Rally (Hard): get a "Clear" or higher rank in Sudden Death Rally (Normal)
Wisp Shoot (Easy): get a "Clear" or higher rank in Coin Collector (Easy)
Wisp Shoot (Normal): get a "Clear" or higher rank in Wisp Shoot (Easy)
Wisp Shoot (Hard): get a "Clear" or higher rank in Wisp Shoot (Normal)