On this page of our guide to Batman: Arkham Knight you will find information about all destructible objects located on Miagani Island. Breakable objects are one of secrets (collectibles) available in the game.
There are fifteen breakable objects to destroy on Miagani Island. Eliminating them all will complete three new Riddler's puzzles (solved puzzles counter will increase every five destroyed objects).
Use Batmobile's 60mm cannon on the objects. They are painted in red and can be found mostly on building's walls. You shouldn't have much trouble with finding them, help yourself with zooming the screen.