How to most effectively handle the strongest units fielded by Cerberus and Reapers in co-op mode. Gold difficulty is assumed, hence these strategies apply to all difficulty levels.
These monoliths are frequently heralded as the toughest enemy to bring down in co-op, but once you start handling them the right way, they're nothing but a slow target that you can patiently wear down.
The Atlas features a powerful shield and, under it, armor that while at first glance seems like another heavy layer, is pretty easy to bring down once you've chewed through the shields. The best ways to bring down the shields are simply being patient with using Overload and Shield Drain over and over again. The Atlas moves slowly, so take your time with it. Sit behind hard cover, and keep spamming Overload and Shield Drain. Fire some rounds every now and then. There are usually other enemies around, however, so the Atlas' slow speed allows you to bring down its shields slowly while taking care of more immediate threats. Just make sure you always have heavy cover!
Once the shields are down, the rest is easy enough. Using Warp in combination with detonation effects, especially Reave due to the added damage, is one sure way of tearing down armor. The most efficient way however, is having a teammate using the Widow or Black Widow anti-material rifle(s). If an infiltrator fires a cloaked shot against the Atlas' visor, it only takes 3 - 4 such shots to bring it down. Always aim for the visor, however, as it does significantly higher damage!
The Brute is more of an immediate threat than the Atlas. While at long range, line up your shots and take the time to combined biotic powers. Warp and Reave are both powerful against armor, and you should always have at least one of them active. This applies especially to Warp as it increases the damage done by handheld weapons against armor, and seeing as how all the Brute has is armor, Warp is a sure bet. Beyond that, once more, Widows and Black Widows are a very efficient way of bringing them down. Assuming you're still fighting it at long range, take the time to line up head shots as it significantly increases the damage dealt.
Once the Brute comes close enough to do a charge (roughly 20 meters in-game), this is when you need to start directing all your attention towards it. Keep using Warp / Reave and keep hitting it with your sniper rifle, and make sure your wingman (on Gold difficulty you should be working in pairs, rarely alone or all 4 in the same place) is shooting the Brute as well. If he makes the distinct charging preparation motion, i.e. takes a step back so that he can kick into a brutal charge, make sure you have space to manouver, and be ready to do a sideways leap. Time it so that when the Brute is mid-charge and 7 - 10 meters away, you do a side-combat roll to avoid the charge. At this point, he is at point-blank range and you need to bring down all you have to take him out fast.
These are arguably the most disrupting and dangerous enemies on the field. With their strong barriers and armor coupled with an instant-kill ability in melee, teleportation / blink ability, nova explosion ability and biotic missile, these are a threat at any range. However, you do not want to fight them in close quarters! That's where they can use a biotic nova to inflict massive damage, or to grab you to instantly kill you. Unfortunately, close quarters is something the Banshee's are good at getting into, due to their teleportation ability.
Like the Brute, you absolute want to fight the Banshee at long range. Go for headshots all you can due to the damage multiplier, and keep chaining bioitic abilities for detonations and to wear hear barrier and armor down. Often the Banshee forces you to stay on the move, at which point many stop shooting her as they're moving, but this is one of the cardinal mistakes when fighting Banshees. You need to keep firing! If only with a warp or even a single bullet every 2 seconds or so, you need to keep hitting her with something to make sure her barrier doesn't regenerate. It is very strong, and if you bring it down for then having to bring it down again, you will most likely get swarmed by other enemies.
During the last waves (8, 9, 10 and 11 (extraction)), these are the times where you should have saved your missile launchers. If a Banshee appears in wave 10, fire a missile at her to take her down fast. There will be so many other enemies that you will hardly have the time to focus on one; the Banshee. In the end, the most dangerous attribute of the Banshee is the amount of time and attention she reserves. While you might be able to bring her down after 15 seconds of focused fire, that is all a swarm of Cannibals, Marauders, Husks, Ravagers and Brutes need in order to close in on your position.
Up until waves 9, 10 and 11, focus-fire the Banshees down. During these latter waves, if you are being overwhelmed by the rest of the Reaper forces, spend your missiles to bring down the Banshees. If you do decide to send a missile flying towards one, however, make sure you time it right. If she starts teleporting, you'll be very lucky to hit her with a missile. You need to interpret the trajectory, and this is by far easiest after she is just done teleporting, or when she is busy using a biotic nova.
In the end, focused fire, intelligent manouvering and teamwork is what brings these heavy units down. Through co-ordination and tactical awareness, they are nothing but a perfectly manageable hinder to overcome for full extraction. - Moliat