Took me a while to get to grips with this map, but now I fear it not. My standard squad aces it (nearly) every time.
1 x sniper + 1 x Rocket launcher stay near the Firebird, crouched. The sniper has reaction fire on, the rocket guy can't, but aliens love leaning over the rails over a turn break. RL's get suprisingly accurate with a practiced operator firing them.
1 x Assault rifle and the Shotgun guy go left, to hit the left stairwell. The other 2 ARs, the MG and the Grenade launcher go in the front door. 1 x AR and the MG peel off and go for the right stairwell. The last AR and the GL draw the main staircase, and proceed with extreme care, because aliens can pop out of those doors, and the GL is loaded with explosives so no reaction fire.
If you've timed it right, all 3 groups hit the same floor at about the same time, 1 from each group can hit a floor simultaneously (and from 3 directions) to clear it, and leave a guy in the stairwell preventing unpleasant surprises.
Using this method, I find that the sniper / RL will usually pick up a kill or two, and the GL and AR in the main stairwell see most action, but occasionally you get aliens in all the stairwells, and clearing obscure corners around the main stairwell can be a pain.
The critical thing is careful use of the GL. Yes, you do need to make sure you are in EXACTLY the right square before you try to put 3 rounds through a door above you, otherwise they come roling back down and explode at your feet. Not fun