What are requirements for a "marksman headshot" points?
Solution 1:
From my experience you can only get the marksman bonus when using the sniper class. I've gotten the bonus using a shotgun while using the sniper class.
Solution 2:
To my knowledge the marksman headshot bonus can only be achieved in the sniper class. Its basically extra points for killing people that are quite far away with a headshot.
To get the bonus your target has to be over 100 meters away and then every meter over 100 will get you another point. So if you killed someone 101 meters away you would get a +1 Marksman headshot, killing someone 200 meters away will give you a +100 marksman headshot bonus etc.
As far as I am aware the highest bonus you can get from this is +500 (although I cant confirm this because thats only from personal experience and never getting higher than that).
A little tip for achieving these is to hold down the fire button once you have fired the sniper rifle - this will keep the scope open so you can follow the path of the bullet and how much it dips. This will make adjusting for the second shot much easier.
Solution 3:
A marksman headshot is the first shot in the head from a greater distance than usual. How much, I really don't know. You can get it with any weapon with sufficient range.
In order to make the shot count as marksman headshot, it needs to be the first shot and it must be a head-shot.
If you shoot multiple bullets and hit the body before the head, no matter how far he is you are only getting the normal headshot points.