While going for this achievement you can also obtain the "PULL NO PUCHES" achievement.
Go into the fight now menu and pick your fighter and oppenent. It doesnt matter who you pick. Before the match, turn all the stats for both fighters down to zero. Start the match and just beat on your opponent. The game keeps track of how many and what type of punches you throw and you can track your stats in the pause menu. Keep throwing your JAB and eventually you will land 250 of them.
It helps if you mix up your puches, makes it go a lot quicker towards getting the 500 landed punches that you need. It should take you about 4-5 rounds. THE ACHIEVEMENT DOES NOT UNLOCK TILL AFTER THE MATCH IS OVER.