To be able to destroy buildings you need to play Raid missions. These do only pop up once in a while in theater of war when your faction is trying to disable a supply base. You need to play as the attacking faction.
In each raid mission there are a number of destroyable buildings highlighted on your map as Uplinks would be done in normal games. They are protected by some sentry drones. A good strategy is to take one Infantry, to storm buildings and kill entrenched Engineers, one or two Transports to shoot down Helicopters, and for the rest only tanks. Depending on the upgrade level of your tanks you can opt to take only one transport as escort since you can take down choppers with combined secondary attacks of your tanks.
Keep your tanks together and attack a building. Try to choose one where you can then easily proceed to adjacent buildings without having to drive much around. Drop your Infantry ahead of your tanks and fortify a building or put them into cover. If your enemy should fortify Engineers, have your Infantry storm the building to rout them out or Snipe them before your Tanks arrive. Engineers in buildings are quite resilient even to the tank's secondary attacks.
Even if you should loose, with this strategy you should be able to destroy at least one or two buildings per match! Rinse and repeat until you get the achievement!