Airbus Helicopters holds the record for the highest take from Mount Everest's summit, they didn't play around with anything less the highest point of earth.
But ok, a sidewinder shot from a Apache flying at the top of his ceiling should do the job as well. My personal pet theory so is, that some USAF pilot wants to become a fighter ace of aces for balloons and is using his political connections within the USAF and the Pentagon to lobby for enough balloon shoot downs to get there. Come thinking of it, maybe it is the USAF fighter pilot community launching those balloons themselves???