This is one of the more time-consuming achievement as you must connect with 500 total Super Arts. Using the Cross Gauge you can immediately unleash a Super Art such as Ryu's famed Shinku Hadoken or Kazuya's Devil Beam! The Tekken characters also all have original Super Art techniques! Example of a Super Arts from the Street Fighter and Tekken side would be:
Ryu's Shinku Hadoken: +
Raven's Doppelganger: +
Asuka's Kishin Enbu: +
Much like the method for performing EX moves you can use the Special Attacks to use a Super Art at the cost of no meter! When charging Ryu's Super Charge attack (which is Shinku Hadoken) continue to hold punch after the red lighting sparks on him and it will release on its own once it reaches the max, releasing his Super Art!
To check your progress for this achievement, go to Player Data at the main menu. Select Player Records and scroll down to see how many "Super Arts Connected" you have to keep track.