Prototype

This is much more easily done going after Hives as they have much weaker defenses against you if you come after them in a tank or helicopter, which you will want to do to take down the hive quickly. So just steal a tank or helicopter, find an infected zone, get to the hive in the center, and destroy it. If you go after bases, follow the same strategy: grab some heavy weaponry and blow up the base (from the outside, not inside like you did during the "Escape the Hunters" mission at the start of the game).

You can track your progress under the Statistics -> Infected and Military pages on the pause menu.