The use of explosives makes it easier to attain this achievement/trophy, as one explosive can kill several monkeys, while the player can concentrate on gunning down other ones that are perhaps out of range of the grenade. This achievement is easily obtained in the corridor (seen in the video screenshot below) before entering the Nova Gas Chamber room. Before entering the doorway to the gas chamber room on the left, directly in front should be stacks of cages with exactly 7 monkeys. A single grenade should easily kill 5 or 6 of them. Simply shoot the remaining monkeys for the achievement.
Also using a grenade lanter can give you the achevement with only using one shot.