[SPOILER] Tips on beating brutal campaign

This mission sucks. The key is using your laser cutter to kill enemies. Target templar->colossi->immortals in that order. You might need to target archons too in the early game. Always target the first wave that comes out first, as waves that come out after it pause for longer before attacking. DO NOT WASTE BEAMS ON REGULAR UNITS. You'll get stuck having your beam shoot a ton of stalkers when it could be speeding up the map or hitting more valuable units. All the regular ground guys die to siege fire anyway.

For the southeast, I walled in the area north of the expansion with planetary fortresses, siege tanks and scvs. The area to the northwest is much harder- bunkers and siege tanks were the best I could come up with. Remember to manually target templar that avoid your beam with your siege tanks.

I tried breaking the protoss with attacks to get the building kill achievement, but it proved far too difficult. Just wall in.

This is the final defense scenario with protoss. For starters, get tons of colossi and keep your phoenixes alive. Colossi are good units in general, and you need the phoenixes to kill the brood lords that harass you occasionally.

In order to survive, WALL OFF YOUR BRIDGES WITH DARK TEMPLAR. They don't get detectors for about 5 minutes, then get them infrequently, then often. When they do get detectors, run in your flyers to snipe the overseer, then rebuild the dark templar immediately. Once you get to really late waves, wall in with a dark templar wall and a zealot wall right in front of them. The zealots will buy you time to kill the overseers before the reach your DTs.

When your lines start falling, withdraw to the inner base where your mothership spawns. Hopefully you have enough carriers to do some serious damage. Fly to the southwest corner of the map (the enemy units will congregate there) where not all the ground units can hit you at once, and the overseers take longer to get to you. Keep killing units, sniping overseers as they come.

If you're having a lot of trouble getting those last kills, spam right click on all the zerglings, who will die much faster than other units.

The final mission, this one has you holding out for a pretty long period of time against waves of zerg.

The key here is that you MUST kill the nydus worms around the map. They appear with boxes around them on your minimap and spawn orange colored zerg instead of the standard purple. You CANNOT hold out against them- I tried, really, really hard with siege tanks, bunkers, scvs, planetary fortresses, nukes... not possible. Thankfully, killing them isn't that hard. I did it with Battlecruisers, but banshees are probably better.

When Kerrigan comes out, she has 1500 hp and some sort of weird unlabeled damage resistance. Battlecruisers are the most effective unit against her, but she'll auto kill a few of them in every fight.

I suggest bunker walls with MANY scvs repairing and siege tanks for support.

When you use your final artifact blast, get all your units onto the high ground with the artifact. Before this happens cover the platform with supply depots and wall off the entrances with barracks (you will probably have plenty of excess minerals). This will prevent mass nydus worms from appearing on the plateau in the closing seconds, which will otherwise kill you.