The achievement is called Blitzkrieg. Complete the mission in 20 minutes or less on Hard Difficulty. I also get the Normal mode achievement, as well as unlocking the secret level. Both of these can be completed on lower difficulty.
I have a detailed explanation of what I was trying to accomplish after my tech and research choices.
Armory: all base upgrades.
Zerg Research: unused
Protoss Research: Ultra Capacitors, Extra Vespene, Auto Refinery, Science Vessel, Tech Reactor
Timestamps (video, not game timer)
00:32 - start by clearing initial marine hellion ball. Attack on marine, let Odin clear.
01:00 to 02:10 destroy all scv;s, the cc, and every factory in Base 2. Try to get as many siege tanks, goliaths, and auto-turrets as you can while making your way out the base.
02:30 to 02:55 -- attack auto-turret, viking, and 3 banshees at Base 1. Barrage the East Starports.
Again, destroy scv's and cc. At 3:48, I just barely barrage the second set of starports before the timer runs out. The starports start to burn just as the scene changes.
03:54 -- hotkey everything. Rally the factory to the Odin, make a tank. Make scv's. Drop a mule. Repair Odin with one scv.
Hotkey the Odin and Thor together and attack right. Research Vehicle Weapons, Level 1.
05:10 -- Bring Odin up the ramp to Base 3. Leapfrog tank to support Odin. Beware of reapers on the cliff, on the tower platform.
Be sure to make an Engineering bay before the 8:00 mark on the game timer.
6:00 -- make turrets to the upper left of your base. Rally a tank to just behind those turrets. Continue destroying Base 3. Remember to use your initial marines to kill the science facility which contains the secret documents.
07:39 -- Secret Mission! Also, remember to make turrets. Southern edge of Base 3 platform. They don't have to be packed together. Mostly, you are using them to deal with the BC cheaply.
08:14 -- trigger the first media tower (base 3). Position your tanks better than I did here, or they will be wiped out.
08:31 -- at 11:00 on the game clock, the banshees will come to your main. Greet them with turrets and a sieged tank. Keep upgrades going. Keep building supply depots.
08:47 -- stupidly, I try to expand.
08:55 -- Tower 3 is done. The BC runs into my turrets. I unsiege and slow push my way toward Tower 2. I should be making depots, siege tanks, maybe more scv's.
10:26 -- I trigger Tower 2 early, and an scv dies for my haste.
10:47 -- a Raven seekers my Thor. Grrr ... Ravens.
10:52 -- evacuate the expo. Tank spotted.
11:07 -- Tower 2 done. Slow push to Tower 1.
11:14 -- I drop Siege Breakers in desperation. I have forgotten to make units at home. Terrible macro, this game (scv's, depots, upgrades).
11:52 -- clear remnants of Base 1.
12:12 -- accidentally triggered Tower 1. Not ready! Scramble scv's out of the way and siege up. Things look not bad...
12:47 -- Where is that Raven???
12:52 -- Oh well, I guess I win. The Odin has too much health on it now, and it's on hold position, capping the point.
The core of my gameplay consists of getting 3 siege tanks, 3 extra svc's, using my initial marines to grab the secret level, and using the Odin to tank and hold towers.
I was derping around at the end because I was looking for the final raven, which always seekers either the Thor or Odin. Beat the mission, regardless. I did not intend to beat the mission so fast. I wanted to set up more turrets, because that raven is so annoying.
Special thanks to RTS Legend. His video is much better, and he manages to do all achievements on Brutal.
RTS Legend: https://www.youtube.com/watch?v=UAAs5jixzeA
On Hard mode, they do not target your scv's.