Verandas can be found on the side of buildings on the main island of New Marais. They can be destroyed by shooting lightning at them. On the main island, there's at least one building on every street that should have one, so it's just a matter of finding them and destroying them. Large objects also count towards this trophy, such as those big gas filled towers inside the power plants; those towers are red in white in color.
Verandas / Fuel Towers
In order for it to count, the “Big Destruction” stunt bonus must appear on your screen, which is by destroying all the verandas on a building or blowing up several of these towers at once.
Destroy 30 verdanas or large objects, and the trophy will unlock. If you know for a fact that you destroyed 30 large objects throughout the game but the trophy still hasn't unlocked, do it again all in one sitting. The trophy should unlock properly then.