EPTFirst of all, raynor has the most life. Always have him lead. Against small unit packs like firebats, marines, and marauders, only use micro and baiting to kill them off. For larger groups of infantry, take advantage of grenade. If there are vehicles like tanks, do use the plasma grenade. In that one room with lots of mechanized units, follow right behind the ares and let it take all the initial hits while your marines clean up the infantry. Make sure raynor plasma renades the mechanized units. You will have enough plasma shots to take care of all of them if you decide that's how you want to spend them. You don't actually need to save these rounds so its fine.
When you reach the brutalisk, have raynor lead so ghosts don't pick off your marines. Take out the units guarding the terrminal and the door. Have raynor plant a charge on the door and have the rest of your marines go back to do the landing zone (to hide). Have one marine release the brutalisk. The brutalisk will take out the guards on the right side of the room before going after your marine. Lure the brutalisk into the next room where more guards and mounted sentries will be waiting. The brutalisk will clear the entire room. Then you simply march in raynor and your remaining marines to clean up.
During the escape, you do have enough time to clear debris and find upgrades. The only big unit you will meet is an ultralisk, so if you have a plasma round left, that's a good time to use it. Use chrono stasis and plant it well to maximize its effect on slowing down the hybrid. The rest is easy.
