Took me a few tries to get the exact timing and placement of this build down so I thought I would share. Here is the download replay link.
This achievement essentially involves cannon rushing either a Terran or Protoss AI. The cannon rush will only work in a map like Agria Valley where you can build cannons outside of the AI base so as to be outside of the range where the AI automatically attacks buildings. If you try to build anything inside of this range (which is roughly the size of its base floor) it will immediately spot you and attack.
Screenshot and instructions after the jump.
As soon as you spawn, move a probe to the location where you want to build the first pylon. Build the pylon but not too close to the wall or the AI will attack. Continue building probes until the pylon is complete and then save up for a forge. Build the forge and continue probe production until the forge is complete. Once finished, cannon once on the lower ground then as soon as that cannon is complete build on the higher ground. Voila, you have successfully cheesed the AI!
Screenshot of pylon and cannon placement: