This trophy is titled "Designated Driver" and it's for using 100 distortion drives. These are the special moves that require either 50 or 100 meter respectively. It's easiest to build the gauge by instant blocking (Pressing back as the opponent attempts to strike, it takes timing but you get used to it relatively quickly) as this gives you 3 each time. Using quick strikes you can build up 50 meter in no time at all. Once you're at 50, you can execute a Distortion Drive by flicking left on the right stick with most characters. This should pop after your 100th one executed.