While in the Neighborhood in MyCareer, go to
Doc's Barber Shop. You can easily recognize it by the striped red/white/blue barber pole over it and it's near the Tattoo Shop.
Once in it, select your haircut, add it to cart with
and checkout with
. You'd need at least 200 VC to acquire a new haircut.
Achievement unlocked.
https://1drv.ms/i/s!Av6y9YAMEBuPhwZ7RUIZZCgvKpUhNOTE: the first time I went to the barber I just changed my facial hair and the achievement didn't pop. I went a second time, got an haircut, the achievement unlocked as soon as I got back on the street.