Start up a 1v1 private match. Set the Time Limit to 10 min (even though that won't factor in your boosting). Set the score limit to 1000 points and the Respawn time to 0. Go to the "Resort" map.
Do not get headshots while using your pistol. A headshot kill is 200 points. A shot in the chest though is only 100 points, which will allow you to get all 10 kills in this single match.
After you score your 10th kill with the pistol, you will pop this trophy.