Before I go any further into the strategies of getting the Wings of Liberty achievements, I just want to say 2 things. The first thing is that I have just finished all the brutal missions on Wings of Liberty and have gotten the Kerrigan portrait (Probably going out and celebrate with an AYCE). Having said that, the strategies are tested and proven.
The second thing to mentioned are upgrades. I have seen many threads and posting concerning which upgrades and researches to get in the campaign mode. I have actually heard of the bug that let you get an unlimited amount of credits by completing research missions repeatedly, but the bug was fixed before I even got the game (Oh well).
I’ll start with the research first. The first thing to say is that most of the Zerg research are utterly useless. Other than Regenerative Bio-Steel, I don’t really use the other research that much. I know that Cellular Reactor is good for specialist units, but honestly I can only think of them useful in Banshees and Science Vessels. This can be circumvented if you plan better with Banshees’ attacks and simply build 2 more Science Vessels. Sure the regeneration is slower than rock erosion, but it does save you a lot of microing troubles with the SCVs. Planetary Fortress can be useful and when combined with Siege Tanks, would make an awesome defense. However, it simply cost too much to build one that you want to spend you cash on something else. Hercules is useful in The Moebius Factor, but useless in all other missions. Fortified Bunker is better since it’ll save you money simply repair the bunker than to rebuild one. To top it off, I don’t use either Hive Mind Emulator or Psi Disruptor in the last mission. However, Hive Mind Emulator is kind of fun to mess around with.
In contrast, every research in the Protoss branch is useful in my opinion. I chose Vanadium Plating for the extra life and survivability of your units; Micro-Filtering for getting Vespene gas faster; Automated Refinery for saving SCVs for better functions; Science Vessel for repairing mechanical units; and Tech Reactor for very fast macroing. Of these research, Automated Refinery, Tech Reactor and Science Vessel are essential for completing most missions on brutal mode.