This is the same as "Close Combat" mode, except with headshots. Enter the following code in the "Secret Codes" menu: 0110 0111. Then go to "Start New Game" and select "Headshot mode". If you want this to go by fast, select the "Easy" difficulty. Play through the story and kill at least the minimum amount required for each section with headshots, and you're good to go. The number will decrease with each headshot you get. There is no headshot requirement on the last level. Also see Catch me if you can.