All single player and multiplayer kills count towards this achievement. You will need to earn kills online or offline, they do not stack towards the same same statistics.
This may come naturally to some players, but not so much to other players. The easiest way to earn headshots is to use your dead eye and aim for the head. This way there is no way you can miss. To use dead eye click in your and the screen will change colour and slow everything down. This will give you time to line up your shots.