This is pretty simple, but all you have to do is own some land with a tree on (pretty much any tree), and cut it down. The easiest way is with a chainsaw. Press select and open the shop menu. Press RB to go to the TOOLS tab, and select the Chainsaws option. Buy one (they cost 1000), and back out to the game. Go close to a tree on your land, press up on the D-Pad to activate the chainsaw, use LB and Right stick to rotate it sideways, and move around near the tree until a green circle shows through the tree trunk (if the circle is blue, you just need to adjust a bit). Then press and hold B to cut until it finishes automatically, it takes a few seconds, and the achievement pops!