You earn this achievement by causing a building to fall below the target level. It doesn't matter what letter grade you get. You can get this by starting on an easy difficulty (Casual, for instance), but beating the first level on Expert isn't hard, either. The best thing to do is to combine this achievement with Ace:
Check out my A+ expert solution for 1-1 here: http://www.4shared.com/photo/YjJS_zpu/P1-01X.html
or you can see my solution for other levels here:http://implode.4shared.com/
The achievement pops when the score shows up, which is when it decides that you have successfully blown up the building.
If you have any questions or have any trouble duplicating my results, please let me know!
Warning: This achievement may be glitched if you used the trial version or created a custom level before you destroyed a building. If this happens to you, uninstall and reinstall the game AFTER you have all the other acheivemetns and you'll be able to easily get this.. Thanks MC Damo for catching this.