As with all Par Times, go for this on Easy difficulty.
I'd recommend using dual SMGs for the rush, but only shooting one at a time (at least for non-elites). After the first door blows, rush through until the first boarding craft room. Don't stand too close to the door as it blows as it can hurt you. Also, I would recommend using the old graphics as I got a lag spike when I rushed the door on HD mode.
Clear the boarding craft room and wait for the doors to get blown. Again, this can kill you.
Clear the next boarding craft room and wait for the doors to open, these ones don't blow up so you can wait by them. Continue on through the armory. When you reach the end of the plaza area, you can jump on the barricade at the back and through the window. It doesn't save you much time, so it's not worth it if you don't make it first try.
You can rush past Miranda and Johnson; you don't have to help them. Continue on until the cargo elevator with the drones. Skip the drones and run down the slant. Look back and kill a few drones so the door opens, and kill or rush past the enemies that come out.
Kill all the Elites outside to get the door to open. Then, clear the final room to get the level to end.
I wish able to finish the level in less than seven minutes.