I once did come up with an upgrade/research/mission order strategy that allowed me to play through Brutal in a single play though, so it is feasible, but like Diamond Dave said, you dont have to; you can just keep replaying missions in different combos to best set you up for a particular mission. The achievement system doesn't care how you do it, just that it gets done. But as far as the missions mentioned here... things that worked for me:
The one trick to the laser drill that messed me up initially is the proper use of the shift right-click.
Once you have the drill selected, do NOT hold shift for the FIRST right click.... do a 'bare' right-click on the first target. (This pulls the laser drill away from the temple door and onto your first target.) THEN hold shift for the rest of your targets. (That will set the laser drill to kill your targets one after the other.)
The reasoning is that if you hold shift for the FIRST target, the game engine interprets that as a sequential command thus it thinks you want to kill the protoss target AFTER the temple door is finished...
If you can get that down, then every time you see the "!" ping on the minimap, start wasting the protoss attackers in the order described in previous posts.
Also, if you have the Concussion Shell upgrade for marauders (the one that slows enemy movement), putting 1 or 2 in a bunker at each ramp will have a psi disrupter like effect on the attacking ground protoss. That plus the bunker upgrade that increases the ranges of the units inside (Projectile Accelerator) will allow you to slow the protoss down well before they even get to the ramps.
I find that on "A sinister Turn" (2nd protoss mission), the faster you can get the templar archives in the eastern base, the sooner you can use Feedback on Maar which essentially neuters him by negating his one shot kill spell which he starts using after a few reincarnations. I keep just two high templar between the two ramps and every time Maar gets just up to my cannon line, I Feedback him and my cannons wipe him out. No need to even keep a garrison at my main base. So I move everyone to the former eastern base for more economy (which Maar never attacks as long as you don’t lead him there).
I am a fan of siege tanks on Train Robbery. If you can purchase both of Swann's tank upgrades (or at the very least the Maelstrom Rounds) and hire Siege Breakers (mercenaries), the mission is very doable. I put all 4 Breakers on the west most outcropping of my base (where the 1st diamondback was) with a couple SCV for repair. Note: come up with a way to protect them from aerial spotters (personally, I bring vikings to the mission as well). If you can do that, they will seriously damage the escorts and trains on the top 2 tracks AND they will completely WASTE the kill teams because they don’t have high ground vision.
The only mission I hate on brutal is welcome to the jungle. I beat it once after countless tries and probably will never try again. Even engine of destruction, which I used to not like, is easy for me now, even without trapping the odin... but not that blasted welcome to the jungle.
Edited by Leviathan on 8/17/2012 12:49 PM PDT