Use dead eye and manually fire your gun. I found that your gun reloads automatically, but it doesn't reset the challenge counter. Also, best place to do it is at hideouts where you only fight a few enemies at a time, like Pikes Basin.
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Theres a youtube video that I followed to do it. Basically go into a bar with a high ammo capacity gun, and take cover behind the bar. Then point your weapon at everyone and they all draw on you. Then pop up and disarm them one at a time. The video suggests emptying all but one clip of ammo from your gun but I did it in 6 separate dead eye bursts and it wasnt a problem for me.
"At a moment like this I think of my father's last words." Which were? "Don't son, that gun is loaded!"
Gaptooth Breach gang hideout. When you get into the mine enemies come at you1-2 at a time. Use the Mauser pistol and manual dead eye. When you shoot a gun out of an enemy's hand let him pick up or pull out another weapon and repeat.
"Getting lost in the light is more than never being found." - Gordon Downie
Search Youtube for 'sharpshooter rank 10' there are a couple of good videos. I got it doing the hideout in the mines in New Austin. Clear the outside, then head in. Use dead eye and always keep LT held down. Repeated disarms from the same enemy count towards the total. Just camp-save near the mines and keep trying. It took me about four tries until I got it. Good Luck!