You have to get a KILL with both the primary and secondary weapon from each kit AND also a grenade kill. A KILL is 5 points, a DOWN is worth 4, and if you finish him after after a DOWN you get 1 more point. Make sure you finish him off or it will NOT count.
There are 2 special weapons, a RPG and grenade launcher. They are found laying around in each map. If your unsure were they are, ready up before everyone else and you can explore the map until the game starts.
I recommend picking a kit, and sticking with it until you are sure you have the kills you need. Then move down to the next kit and do the same thing until the achievement unlocks.