What is a strategy to earn the best defense achievement in StarCraft 2?

I have been attempting to earn the Best Defense achievement in StarCraft 2.

The Best Defense is an achievement earned during the third mission of the Wings of Liberty campaign: Zero Hour. The goal of the mission is merely to survive 20 minutes, while awaiting evacuation. However, the achievement is earned by destroying 4 Zerg hatcheries during those 20 minutes.

Thus far my strategies to accomplish this goal have failed. Has anyone devised a winning strategy to earn the achievement?

Build a refinery first, then add a bunker next to each of the existing ones by the bridges. Build a billion SCV's , a billion supply depots, and 4 barracks (one with tech and 3 with reactors). Tech barrack should only produce medics other three should only produce marines. Don't worry about stranded rebels, keep all troops near bunkers until about 9 minutes are left. Attack the Zerg base at the top left of the map with a force of about 30 marines. concentrate fire on Zerg troops until there are none then have half the marines fire at each hatchery. THE MOMENT you have destroyed BOTH hatcheries, immediately pull your troops out into the corner away from the Zerg base, do not destroy anything further. Keep building troops and after a few minutes send a second force of roughly 20 or so troops to meet up with the first force. The hatcheries should have respawned by now and you can go in and destroy them both with little resistence a second time to earn the achievement.

This isn't an easy one to earn. It requires decent micro of your troops, while still focusing on the macro of getting more troops. There isn't much more to say besides "play well", but I'll give a couple of general strategy hints:

Get an SCV or two out by your front line to help with repairs. You should also be able to easily get the "don't lose a building" achievement at the same time.

Get 3 SCVs on each minerals. Get those minerals coming in as fast as you can.

You might discover that money is coming in faster than you're spending it, get another barracks to pump out more troops.

One of your barracks should have a reactor core, and the other a tech lab. 2 marines per medic. As soon as you've got a decent force, (which should probably be < 5 minutes), head out. I'd recommend going around the map in a counter-clockwise fashion, i.e. head out north east, rescue the first group of trapped units, then head in the general direction towards the second group of units, then the third, killing all Zerg along the way. New troops that you make should head to your group soon.

The enemy gets stronger as the time progresses, so the sooner you leave the better.