Targeting Penguin's Bird Cages
On continuation of the game I have discovered that to interact with objects using your gadgets, you must have first scanned/analysed them in detective mode.
Once you have scanned a bird cage, it will become targetable with your batarangs. This also applies to Joker Teeth, Black Mask's masks, vents, circuit breakers and wooden piles/weak wooden barricades (with the respective gadgets).