1. Build an Armory and Engineering Bay
This mission introduces the Medivac unit, a transport vehicle that also serves as a Medic. This mission also follows a pretty strict time limit, as you have to beat Kerrigan to the Data Vaults. Get the SCVs going as usual and build an engineering bay and an armory, begin researching infantry weapons and armor, and ship plating.
2. Begin creating Marines and Medics, build small defensive line
Build a small defensive line at your base's entrance and keep a few marines at your base to deal with the periodic attacks from the Nydus Worm near your base, make sure to destroy the canal quickly after it appears.
The Medivacs are useful but they have heinously low armor and can quickly be destroyed by Spore Colonies or Hydralisks, taking all your precious troops with them. be extremely careful when moving around the map with a full load of troops.
3. Destroy the first Data Vault and rescue the infantry
Once you've got your production going, load one of the Medivacs with marines and leave the other empty. Rescue the troops marked on your map and have all of your forces fire from the high perch to destroy the first Vault. Load everyone back up and return to base.
4. Build additional Medivacs and infantry
Begin building 2 more Medivacs and some additional troops to fill them, feel free to use the mercenaries as time is important here. Make sure to build a few Vikings to escort your Medivacs, while there aren't a lot of aerial units in this map, the Medivacs are totally defenseless and nothing's more annoying than losing your platoon of troops because you sent them in unprotected.
5. (Achievement) Kill the enemy Brutalisk
Load every one up and take a trip to the middle of the base where the optional Zerg research Brutalisk is. He's not difficult to kill and clearing the spore Colonies out here will give you a straight line to the last Data Vault, so it’s worth it. A Medic, a few marines and marauders should be plenty to take care of the Brutalisk.
6. Destroy the second Data Vault
Approaching the second Data vault can be dangerous, as it's covered heavily with spore colonies. Take your medics up behind your base and have them loop around on the edge of the map to the corner nearest the second Data Vault.
You'll have to drop your troops off at a little distance for safety's sake. Have them proceed down the narrow corridor taking out the Spore Colonies, then loop back around and up to the base.
Activate the troops here to bolster your numbers. Be careful of Kerrigan as you may run into her as you're looping around up to the base. Once the Data Vault and spore colonies are destroyed, send your Medivacs in and return to base for repairs and healing.
7. Destroy the final Data Vault
The last data vault is much easier by comparison. Fill up the four Medivacs with all the troops you can muster and head in a straight line to the point indicated in this pic:
You can safely deploy your troops here, and its only a small distance to the last Data Vault.
Storm in with your units, a dozen marines a few Mauraders and 2 Medics is plenty, and take the last point to end the mission.