STAR WARS: Battlefront Classic Collection

This can be achieved offline playing against bots. You can check how many medals you have at anytime by doing the following. Select profile>Main menu>Options>Career stats. To obtain this achievement you must earn 32 Marksman medals.

Or in other words get 6 headshot kills in a single life without dying 32 times.

There are 4 different medal categories

Green: 0-3
Veteran: 4-32
Elite: 32-63
Legendary: 64+

To reach elite Marksman status you need to get the Marksman medal 32 times.
(Marksman medal - Get 6 headshots with a Sniper Rifle in one life)