Door covering can work, but only if you've got a signifigant portion of your squad availible to do so. Even then it's still a gamble.
Basically when it comes to the hardest difficulty level, you want to use only the most powerful weaponry availible. Anything less just won't cut it due to the signifigant damage reductions your equipment suffers at this setting. That said, the rocket launcher, plasma/frag grenades, particle beam weaponry, and full auto/spray modes are easily the most useful weapons and weapon settings. Everything else is largely ineffective. Kill the aliens before they kill you, and always be mindful of the fact that the aliens 'cheat'. They always know where you are. If they have enough actions to move and take a shot at your soldier, they probably will. Do not depend on the aliens inaccuracy to save you, especially when they get particle beam weaponry, because such inaccuracy simply does not exist at this difficulty level. You must rely on cover.