When you've finished the tutorial you'll be given full control of your island. If you move the camera to the right you should see a large patch of terrain with some rocks and palm trees on them. Click on one of these and select the remove option.
Your engineer will remove the object in roughly 15 - 45 seconds.
If you need to, you can use the gold bars to speed up the engineers and buy supplies to remove the rocks/trees with (which is what I did as I have no intention to play this game for fun).
As soon as the eighth piece of terrain has been removed, the achievement is yours!