In the upper left in the arcade mode there's challenges, that change every match or when the player completes them.
The fastest way to get this is to just try to do what ever is asked.
Jump 3 times - the easiest, just do it.
Dash/roll 3 times - hit R1 three times.
Hit opponent with a special move - this is a special move, just hit the opponent with one, even if she blocks it counts.
Hit opponent with an EX move - this is the extra special move, basically do a special move with both buttons (LK and HK or LP and HP) together. Not all special moves have a EX mode, but on the move list they will tell you which counts. This requires a power bar as well.
Hit opponent with 5 normal attacks - They can be blocked. Just don't use special moves.
Hit opponent with a 3 hit combo - this one is harder, if you know the character figure out a 3 move combo, if you don't feel free to wait til the next round.
Hit opponent with a desperation move - This is the super move ( the one listed on the page AFTER special move)
Drive Cancel - I never could do this one apparently it's a counter/cancel move. But honestly just skip this one and wait til the next round.
Honestly you can either ignore this and get it while you play the game and get other trophies or go after this right away, either way you'll probably get it with in your first or second hour.