This trophy is titled "I Got Your Ammo!" and requires you to drop 100 Ammo Boxes.
In order to drop ammo boxes, you must be playing as a Rifleman in an Infantry Unit. This is the only unit capable of deploying ammo boxes.
Once you spawn, switch to the ammo box with R1 or Up & Down on the control pad. Press L2 to bring up the deploy reticule when the ammo box is in-hand. Move the gray box around until it turns green and then hold down R2 to deploy the ammo box. Once deployed, you will have a five minute cool down before you are able to deploy another ammo box.
That means 12 ammo boxes can be deployed an hour. So overall, this trophy will take eight hours and 20 minutes to complete if you're fully paying attention to your time and on top of deploying the crates.