This is apparenlty a poorly designed/documented mission, it tells you what to do and yet it does not.
You have to move ALL of your guy's including the doctor to the far platform.
OK now for the rest of you. This is how I do it I'm sure it is not the only way. I have mostly sniper rifles, and a flame thrower. Move the doctor toward the switch. Move the flame thrower with him. Leave two guy's on the platform. Move one onto the weak bridge. And if you have anyone else move him by the doctor.
The Cy'Coo can only be killed in defense mode. So take them out when you can. Move the platform sending two guy's around the back of the three towers to kill the enemies there, and to pick up some points. The guy on the weak bridge needs to move up so he is not on it, but only by one step. Be sure to move your guys or at leat the doctor every turn. Even if they do nothing or they'll be hit from the towers. Move the two guy's off the platform, hit the swithc again, when it get's back cover all but the edge ith flames. This forces the TWO Gore Ther to move toward the guy that is on the other side of the weak bridge. Can you gess what will happen? Whil they are moving the guy's from the other end will be moving to the guy on by the weak bridge. Move the flame thrower and any other avail able guy's that way to help him out. Killing the last Gore Ther will be up to you. I suggest getting him to go down one path or the other so you can easily get behind him.
Now, that should take care of all the enemies. If the Guy's on the platform are not dead just keep moving. Send someone back to hit the switch to bring the two guy's that went on the scavenging mission and simply get them ALL to the platform.
You will earn a commendation from this mission.