For this achievement you must perform a total of 500 special moves. Special moves are a common staple in any Capcom fighting game where you launch projectiles or perform special attacks against your opponent. Every character has a unique list of Special Moves under their command list all of which can be done with a simply rotation and push of a button. A lot of the Tekken characters have special stances within there special move list that match that of their styles from the Tekken games. Here are some simple examples of special moves from Ryu's repertoire:
For each special move to count towards this achievement it must physically make contact with the opposing character when they are not blocking. This can be unlocked naturally across every mode except for Challenge Mode and Training. You will most likely receive this while working towards other achievements and will pop after the match you performed your 500th special move on.
To check your progress for this achievement, go to Player Data at the main menu. Select Player Records and scroll down to see how many "Special Moves Connected" you have to keep track.