You can get this on any campaign or Special Ops mission. The best places to get it are missions where you start off with a weapon that has either a grenade launcher or shotgun attachment. First, just kill an enemy with your primary weapon. Then kill an enemy with your grenade launcher or shotgun attachment. Then switch to your secondary weapon and kill another enemy. Then pick up another weapon off the ground and kill another enemy and then do the same thing with another gun you picked up off the ground get the achievement.
Some people have been able to use their knife as one of the weapons but others have used it and have not unlocked the achievement. If you use the knife and don't unlock the achievement, just pick up another weapon from the ground instead.