The fighting in the game is fairly straightforward: Hold LT to target your opponent/get into fight mode, press A to punch, press X then A to counterpunch an opponents attack and press Y to grapple.
You'll have a chance to practice during a fight in your patrol cases but you cannot get the achievement here (as you will not be an LAPD Detective yet).
Your first 2 opportunities in cases will come in 'Fallen Idol' if you can drive to the hotel fast enough (don't let your partner drive, it skips the fight) or a fight in 'The Red Lipstick Murderer' at Jacob Henry's apartment.
I would recommend counter punching for serious damage followed up by a quick punch - a couple of these should do the trick. If you get hit once, you'll lose your hat, so you have to fight defensive. Opportunities will also arise in the street crime cases and throughout more story missions.
The video will help some as well.