If you are still in need of this solo achievement and the 100 sniper kills achievement, I have a quick set up for it. Get together 5 gamertags, whether its with other people or other accounts you may have. Now go to:
-Public Private Match
-Custom: Infinite respawns, Victory: 10 points
-Time limit: 5 minutes
Now all you have to do is the person who is going for the achievement get 10 kills with the sniper rifle. Since you need to win 10 solo matches, you will be getting the Sniper achievement the same time you get the Solo Verteran (10 matches x 10 kills = 100 kills).