Here is the full list of all 13 Barrels Up achievements.
You're ranked 1st against your friends
You've managed to get to wave 30!!!
Score over 50,000!
You've managed to get to wave 20!!
You've managed to get to wave 10!
Managed to gain a direct hit streak of 10
You scored over 9000!
Get a streak of 7
You hit a Freeze target
You scored over 1000!
You've hit a power up target!
You found the Sombrero
Blow up 4 Barrels with a single stick of dynamite