This can be obtained on Chapter 1 - Level 8 (Lumberjack) when you first get the Axe Power Up (Green).
It is fairly simple to get, but I missed it at my first attempt. Its best to take a low power shot to collect the power up and stop at the edge of the trees, just to the left of centre, as there seems to be a greater density of trees here. Then take a full power shot upwards towards the finish. This should take out 7 trees and pop the achievement. If not, just restart level and try again.