A fast and easy way to get this achievement is to fast travel to the first challenge location (Bomb delivery #1). You can do this by going in the Log section in the menu (by pressing ESC or
) and selecting the challenge "Bomb Delivery #1" in the latest challenges. This is the first challenge in the list.
After fast traveling there, you can instantly see the blimp in front of you. Only thing to do now is to get to a rooftop close enough to the blimp so that you can shoot and destroy it. For this I used the upgraded Dirty Harry gun, which can destroy it in one shot.
One done and 24 to go, so fast travel back to the challenge location to respawn the blimp and repeat this until you hear that magical sound congratulating you on a job well done
Without loading screens a single blimp can easily be destroyed within 30 seconds, depending of course a bit on your skill and speed of traversing Sunset City.
For people more inclined to a video instead of text: