For this achievement you must finish 300 rounds by hitting your opponent with a Super Art. Super Art inputs differ depending on the character but all of them cost 2 Cross Gauge bars to use. Some Supers are invincible and others are not. What makes Supers stand out though are their damage and the fact that you can cancel a chain combo into them. Some common examples of Super Arts would be:
Ryu's Shinku Hadoken: + ()
Kazuya's Devil Beam: + ()
Bison's Knee Press Nightmare: + ()
Once you have your opponent's health gauge down to less than 25%, connect with your Super Art to finish the round. The screen should say K.O with flames covering the screen followed by the words Super Art Finish on the left side of the screen when you do this.
Go to Versus with a 2nd controller. Pick Ryu and after selecting your Gem Unit set your handicap to 75% to avoid perfects as it will not count as a Super Art finish. Next, select the 2nd players characters and set their handicap 0%. When the match starts do a Hadoken but DON'T let go of your punch button! Keep holding it until Ryu throws out his Super Art version, the Shinku Hadoken. Repeat until this unlocks after the match.
Also, see The Cross Revolution for more info on obtaining this achievement. To check your progress for this achievement, go to Player Data and then Records from the main menu. A full guide on how to perform everyone's Super Art can be found here. You can also check their move set from the pause menu.