I got the achievement with a safe but somewhat boring and slow strategy: Turtle up with a boatload of siege tanks and missile turrets, and float a command center up to the northwest corner of the map to get vision on the Protoss buildings. Use the cannon to pick off the buildings (and the defending units), stopping to take out the archons/immortals/colossi that gather outside your base when they appear. Your tanks can handle zealots and stalkers, so don't waste cannon time on those.
The Protoss will continually rebuild the structures that you destroy, so you can probably just work your way back and forth in the top-left area of the map until you've blown up enough structures to unlock the achievement. Try building two command centres, and bring one back to base for repairs when it gets heavily damaged.
When controlling the cannon, remember to use the Shift key to queue up multiple targets. This will give you a few seconds to do other stuff around your base while you wait for the cannon. When scouting structures with your CC, you can use the Hold Position (H) command to stop it from moving around when taking hits and losing vision on buildings at the edge of the fog of war.
I'm sure other methods will get the job done faster, but this strategy was very safe and not very difficult.