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.