Keep A Lid On 15G
Complete a brawl without losing your hat as an LAPD Detective or Investigator.

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Cases: The Fallen Idol [Traffic], The Red Lipstick Murder [Homicide], The Golden Butterfly [Homicide], The Silk Stocking Murder [Homicide], The White Shoe Slaying [Homicide], The Black Caesar [Ad Vice], The Set Up [AD Vice], The Gas Man [Arson], A Walk in Elysian Fields [Arson] & House of Sticks [Arson].
Street Crimes: Boxing Clever [Traffic], Canned Fish [Homicide], Daylight Robbery [AD Vice], Bad Date [AD Vice] & Accident Prone [Arson].

In many cases or street crimes you'll be made to fight your suspect/s. When this happens, you'll need to make sure you don't get hit (you can take one punch on some occasions), otherwise you will lose your hat, thus disabling the achievement.

The earliest you can gain this is on the case 'The Fallen Idol'. A little way into the case you'll be following June in your car. You'll then have to follow her into a caf and go incognito. Once the scene is over, you'll be told to rush to a hotel to help another suspect. Once you arrive at the hotel and make it up to the room, you and your partner will be confronted by 2 guys and a brawl will start out.

Your best bet is to just hold X But to block until your opponent has thrown their punches. Once that's done, throw your 3 hit combo but tapping A Button, then go back into a block. It's up to you if you want to try and dodge and counter his attacks but it's a little risky. Once both the guys are down the achievement will unlock.