How to get the hat back on

I think you need to shoot it in the back to deal a fair amount of damage

I sent both my squad members to the right of the starting wall and had them shoot at the sectoids. I lifted the walker and ran to the left flank this allow me to shoot at the walkers weak spot on its back

Hope this helps

Use at least one character with the ability to lay mines, and equip a heavy weapon. When the mutons appear, immediately mind control one to help deal with the other enemies that are around.

Next, pull your squad back into the entrance corridor and place one on either side, out of line of sight of the main area. Have them fill the small corridor with mines while taking care to move anytime a muton drops a plasma field on someone (they can do this through the walls). Try to spread the field out a bit to avoid everything going off at once. You can also drop turrets as far back as possible to add to the damage dealt.

After a time, one of the mutons will try and walk through the minefield (you may wish to use the Taunt special to speed this up). Combining that damage with the lift special (it won't lift them but will keep them still long enough to fire) and hitting them with a fully charged heavy weapon will take them out.

Repeat for the second muton.

It may take a couple of tries to get them appearing with enough time between to reseed the minefield. You can buy a little time by using your lift and mind control abilities to slow the other one down after the first is dead.

Can't deal enough damage before the muton gets to you at the end of the corridor? Save your sticky grenades and use them as well to increase the rate of damage still further.