This achievement is rather simple and straightforward forward but highlighting the first 5 armaments you will use in the Modern Warfare III campaign goes as follows
1. In the mission "Precious Cargo", you will find the sentry turret in the boat when you find your first loadout box
2. In the mission "Reactor" you will find the next 4 armaments with the first one being the helicopter right when you drop in. You will find a mortar strike right next to the self revive on the ground on the second floor of the construction building
3. Proceed to the second helicopter by the "A" building. Outside on the ground will be an additional supply drop of ammo, equipment and the precision airstrike you need to use to count toward the achievement
4. Make your way to the last helicopter and grapple to the roof next to the helicopter and find the Stealth Bomber and use it to take out the 3rd and final helicopter
5. On the same roof, behind the Stealth Bomber spawn, you will find a Bomb Drone. Pick it up and use it and the achievement will pop!
There is also a UAV on Reactor that you can find between the first helicopter and the reactor building