Dead Eye is an ability that will decelerate time allowing you to shoot very fast. To activate it draw your weapon, target with LT and press the right analogue stick RS. There are three levels of this ability:
First level will only decelerate time and allow you to shoot one time
Second level will automatically target your enemies and you will be able to shoot until you will be out of ammo.
Third level will allow you to target your enemies manually (RB) and you will be able to shoot until you will be out of ammo.
This is the bar that will show you if this ability is accessible at the moment. You can charge this bar by doing some spectacular shots (for example: head shots) or by drinking some drinks in a saloon. Later, you will be able to make this kind of potion on your own.