Super arts can be executed one of two ways. Firstly, you look at the input under the character commands. These usually involve some type of direction, and all 3 punch or kick buttons. An example of this would be Ryu, his would be a quarter circle forward and all 3 punch buttons with a full meter. Secondly, you can use the special move that shares this input and simply charge it to the point where it becomes a super. Using Ryu once again if you hold the punch button while using a Hadouken, he will flash once meaning it has become an EX Special and then he'll unleash it as a Super Art when it can't be held any longer.
The easiest way to knock this out in a rapid manner is to go in to a local versus match versus a second controller (Or even an easy AI) and simply spam them. Set the rounds to 4 as you want to reduce load time between matches as much as possible, and I'd reduce your opponents handicap down to 0 percent when going for the Super Art finishes. After this trophy pops, up the handicap to 100% that way you're playing fewer rounds and connecting with more Super Arts.