Wait until you've acquired the Inhuman quest chain quest labelled "Day of the Remains". In this, you will be tasked with aiding the Inhumans and will uncover two Vault Caches, whereas most locations in drop zones will provide you with one. Doing this twenty-five times is frustrating, but it will be much faster and easier than trying to do this normally.
Once you start the mission, proceed towards the objective marker. Once you arrive, you should head over the tanks to your left and a vault stronghold should register on your tracker. Proceed here and open the cache strongbox. Now, proceed to the next objective point, where you will need to rescue two prisoners surrounded by a ton of AIM antagonists. A cache will be opened up for you once you've arrived, meaning you can simply go down to get the box(es) and either rescue them now or simply return to the Quinjet right then. Rinse and repeat this to get your trophy.