This page of the Aliens Fireteam Elite guide offers a walkthrough for Breach, the first mission of the fourth campaign (The Only Way To Be Sure).
Start by going to the new room which contains automated turrets. Inside, you'll encounter some basic Xenos.
Your objective is to supply ammo for the turrets. Destroy further Xenos and approach the turrets to resupply them.
Once that is done, follow the next marked waypoint. You'll encounter some Synths while proceeding through further rooms. Note - Synths spring back to life as you get closer to them, so it is better to destroy them from a safe distance.
In the next large room, you'll encounter a large group of Synths. Eliminate the enemies, and then deal with the immobile Synths in orange uniforms. Stay away from them, as once you get closer, you'll be attacked.
After defeating the enemies, go up. There is an ammo chest, medkit, and a random pick-up on the left. Another battle awaits - approach the door and hack it. . You'll be attacked by a group of enemies after completing the action.
Synths will come from both left and right sides. Fortunately, most of these enemies are basic ones, but as you proceed further, you'll be facing flamethrower-wielding ones. The easiest way to defeat flamethrowers is to shoot the fuel tank on their backs.
In the next room, you'll have to replenish turret ammo once again. This initiates a confrontation with Xenos, coming from both sides. The turrets will help you in dealing with them.
Further turrets will be encountered along the way. Rinse, repeat - replenish ammo and then face a wave of xenomorphs. You'll encounter both basic enemies and Warriors. .
You should be close to a nest - easily recognizable, as there are large amounts of eggs here. As you approach the eggs, small parasites will hatch and jump on you if you're close to them.
To free yourself, you need to press the buttons shown on the screen.
Further ahead, there is a narrow passage from which Xenos will emerge. Use an area of effect ability to quickly get rid of them.
Once the area is cleared, approach the computers. There are supplies nearby - a medkit and ammo crate. If you are ready to proceed, approach the computer and install the repeater.
This will spark another controntation with Xenos. Some of them will stay on the walls, while others will appear from the left, right, and center sides. Beware of agile Xenos, as they will attack you and hide back in the nests.
After defeating the opponents, follow the waypoint. Along the way, you'll encounter an ammo crate, a first-aid kit, and a pick-up. If you are ready, install the repeater again.
In this next battle, you'll be facing more powerful versions of enemies, including Warriors, and Praetorians (latter being even more powerful than former). If a Praetorian begins to roar and stand on two legs, make a dodge and fire at its head.
After the area is cleared, follow the marker to complete the first mission of the fourth campaign.