Instructions
Load your single-player save game. This automatically unlocks four avatar awards added to the game in February 2011.
Go to your home in Beecher's Hope, marked on your in-game map. Go to the attic and open the chest sitting there. This unlocks a T-shirt for your avatar.
Go to Riley's Charge in New Austin, marked on your in-game map. Find the chest in the burned down ruins of what used to be a cabin to unlock another T-shirt.
Hold "LT" and press the right analog stick in to enter Dead Eye mode while fighting an enemy. Hover your reticle over your enemy's hat and press "RB" to mark the hat. If aimed properly, Marston will shoot the hat off your enemy without killing him, unlocking a sombrero for your avatar.