You need to kill 13 enemies in 15 seconds. It seems to me the maximum amount of enemies in a contract is 13 or 14, meaning you basically must kill all enemies within 15 seconds. This is best attempted by randomly firing a shot at the beginning of the contract to get all enemies to spawn. Just count up all the enemies and plan how your shots you will use to dispose them all. Careful not to take too much damage while surveying.
A good long-range gun with a large clip to earn this with would be the Anti-Material Rifle, which costs $350,000 and requires level 13. The actual missions and enemy positions you get are random. Once you have a good weapon, attempt this on a level with a lot of explosive barrels and very little cover for the enemies. Achievement pops after you kill the 13th enemy.
GOOD METHOD: I got this on the contract point to the top left or bottom left of Monument Square. The enemies basically just congregate on both sides of the street near the two explosive barrels. This location is quite easy.