Using the Breach interface is not the most intuitive so here is a quick guide:
First, queue up your agents next to doors outside the room. When at least 4 are in position and they all have at least one movement and one fire point, click the breach button. Now left-click anywhere inside the desired room. This enters the breach planning mode. Now right-click on an enemy to assign that enemy to the current agent. A teal glowing line will appear between that agent and their target. Click on another agent and repeat the target selection process for them. Continue to assign targets to each of the agents, as well as choose what weapon they use by clicking just above their character portraits. When each agent has a target, the bottom middle box should say “Breach Order Prepared”. Click “Confirm” to start the breach.
Keep in mind that breaching imparts a significant damage boost, so even poor weapons can often result in kills using breaches. The Breach tool will show you the projected maximum damage. If using silenced weapons, the breach will not break infiltration mode unless there are enemies or civilians inside the room that are not killed. I can verify that civilian kills will count towards the total of four, as this unlocked for me on a breach of a room with 2 baddies and 3 civilians.