Main Objective: Destroy Forces Before the Nuclear Strike, Breach the Tactical Operations Center
Bonus Objective: Destroy the Science Facilities [0/2]
Old Soldiers: Complete the "Old Soldiers" mission in the Heart of the Swarm campaign.
Nuclear Launch Rejected: Destroy 20 enemy structures before the 1st Nuclear Strike in the "Old Soldiers" mission.
Recalled Down the Thunder: Complete the "Old Soldiers" mission in less than 20 minutes on Normal difficulty.
Clear out the Terran base to the right. Not only will it free up an expansion, there is also a Science Facility to destroy for the bonus objective. Clear as much as you can, because these are free units that you will lose after the nuclear strike. Doing so will reward you with the Nuclear Launch Rejected achievement.
Saturate your base as soon as possible. Warfield will randomly drop nukes on your base and army so spread your buildings and always be mindful of the whereabouts of your army. You don't have to worry about adding much static defense at your base because there aren't that many drops. A few Spore Crawlers will be enough to give you enough time to send a pack of speedlings back to deal with Vikings and/or drop.
Spread creep with your first queen. Not only will it help with mobility, it will give you vision and let you know of any impending attacks. There will be an attack at roughly around 8:30. After you deal with this first attack, it's pretty safe to take that expansion you cleared earlier.
At roughly 11:20 there will be a group of vikings that will attack your base. This is where raptor lings with metabolic boost really shine. They can make it back to your base in record time and if you need to build more they build almost instantaneously.
There's quite a bit to deal with over by the right science facility. You should have a stable economy by now which will allow you to clear it out with a few waves of units.
This level is pretty much a war of attrition. As long as you do damage, regardless of how many waves of units you send, you will be victorious. After clearing out the units in the front of the left base, even returning a while later, the units and the buildings initially destroyed are not rebuilt. Clearing out this base will give you a gold expansion which will pretty much ensure victory from here on out.
Building a mix of units, especially after evolutions, make for very effective armies. The main composition of units used for this level was comprised of zerglings, roaches, hydralisks, and abberations.
At this point you can send wave after wave of units until you clear out the remaining Terran forces.