This achievement is actually a lot easier than you may think. There is always 6 or 7 items in each care package so you only need about 8. Simply look for the plane each time you hear it and head straight for the care package. If you don't know what the care packages are, they are the red crates that the plane drops randomly throughout the match. They are sometimes pretty hot and others will likely be heading to them.
About one in four times though you should be able to get to them if they are close and quickly get everything out of them before you get killed.
They also generally contain a full level 3 kit, bag, helmet and body armour, so you can get the achievement for that at the same time.