To get this you should start a game in single-player on any map.
Hold Q to open your spawn menu and select the Balloon option on the right side. You can select any model balloon for this and I suggest you keep the rope size rather small so it doesn't go outside the skybox.
Spam balloons EVERYWHERE until you feel that you either have 1,000 or get tired of clicking. Spawn in any weapon you'd like and start shooting the balloons. I chose to use explosive weapons from the
M9K - Specialties mod. After shooting or blowing up 1,000 balloons, the achievement will be yours.
