Unlock the following outfits by performing the corresponding tasks:

OUTFIT - HOW TO UNLOCK
Button Man - Complete the Badge Pursuit Challenge. Gives all yours weapons extra ammo.
Chicago Lightning - Sign up for the Rockstar Social Club. Increases your accuracy with shotguns and machine guns.
Golden Boy - Have Cole Phelps get promoted to the Traffic Desk for the LAPD.
Hawkshaw - Reach Rank 18. Allows you to take more damage.
Sunset Strip - Reach Rank 8.
Sword Of Justice - Reach Rank 3.
The Broderick - This was an Amazon pre order bonus. It increases melee damage and resistance to damage.
The Outsider - Reach Rank 13.
The Sharpshooter - This was a pre order bonus with various retailers. Increases your accuracy with pistols and rifles.