To unlock Professional, you must first complete Desperate Escape on Veteran. You can also join a friend who has already unlocked Professional. Doing this will save you a playthrough and the achievement will still unlock. Works best in Co-op, since the A.I. isn't the best partner.
Alright, now it sounds silly to make a guide on each area specifically, since my general strategy was to just run, and kill what's only ABSOLUTELY necessary.
To start out, you should definitely have a shotgun and a sniper rilfe. Start out by running into that little building that has the 2 machine gun ammo and the 1 shotgun ammo. Pick them up, but be careful as it's very dangerous. May take a few tries to get it right. After that, run over to the area near the elevator, and jump up to the top. Stay on the left side (left if you are looking out towards where you came from, above the elevator) The guy with the shotgun looks straight out and shoots the guys that jump up, knocking them off. A pistol works too but does less damage, and you can only shoot 1 at a time. The guy the the machine gun looks out over the bridge, and as guys run across it, shoot the in the legs, beware of leg armor, and then run up to them and press to finish them off, conserving ammo.
Around 4 minutes left, for me, a Red Executioner spawned from the elevator. Multiple enemies with guns also spawned. One will spawn across the bridge, and the other with spawn on top of containers if you look straight out. They don't always spawn when the Red Executioner spawns, but they always spawn in same locations. When the Executioner jumps up, run across the bridge, and primarily the shotgun will take him out, with the machine gun guy covering his sides. A sniper rifle also helps here. Careful as the Executioner will blow up, delivering damage to you, and sometimes a guy will come up the ladder to your right that explodes too.
At about 2 minutes left, when Doug comments on he will be right there, a Reaper will jump down right on the other side of the bridge. Back up as far as you can, having the shotgun guy covering the side, the rifle guy shoots the Reaper when its chest opens up and you can see the gold/white/yellow thing. It stuns him, and another colored weak spot will pop up, shoot that as well with the rifle, and it may kill him or another one will pop out somewhere. Shoot them 2 or 3 times with the rifle and he is dead.
However, another Reaper may spawn, but take the same steps to take him out, or run if neccesary. A good spot to hide for a bit is the corner straight ahead and to your left when you jump down, a box is in that corner. Another Red Executioner will spawn too, but I do not recommend killing this one. Most likely you are low on ammo, and your best strategy is to run to that corner I mentioned, wait a bit, then keep running back up top, then to corner, and so on. You will have to shoot some things though.
NOTE: The weapons I have listed are just suggestions, they are in no way needed, and you may not even obtain them throughout the playthrough. Weapon spawns are random.