Here is the full list of all 14 Balloon Blast achievements.
Join a server
Pop 3 balloons while you don't have one
Pop a balloon while speed boosting
Pop an opposing teams balloon
Drop into a map 10 times
Pop an opposing teams balloon by firing from at least 5 meters
Take the acceleration cannon 15 times
Win a round of at least 100 points without losing your balloon
Make a server
Pickup 15 pieces of debris
Play for 60 seconds without a balloon
Take the acceleration cannon
Get someone to run over your debris pile within 1 second of deploying it
Enter the practice range