Successfully complete the indicated task to unlock the corresponding arena:

Coliseum Rooftop: Successfully complete Solo or Tag Tournament mode two times. 
Endless Planes: Successfully complete Solo or Tag Tournament mode three times. 
Hokage's Arena: Successfully complete Tag Tournament mode. 
Infirmary Roof: Successfully complete Solo or Tag Tournament mode four times. 
Madara Uchiha Statue: Successfully complete Solo or Tag Tournament mode five times.
Temple Courtyard: Successfully complete Solo Tournament mode. 
The Valley Of The End: Successfully complete Solo or Tag Tournament six times.