Call of Duty: Vanguard

Mission 9: The Fourth Reich

As the description says, you need to complete this entire mission without friendly fire. There are really only two possibilities for friendly fire:
 

• Shooting one of the allies you're on this mission with (blue name pops up above them when you aim at them)
• Shooting a civilian in the subway tunnels

I'm not sure if it's just a Veteran thing, but shooting a civilian caused me to fail the mission and reload a checkpoint, so I don't believe that second point is even really an option for voiding this achievement. So with that not a concern, it really just becomes a matter of not accidentally shooting one of your teammates for the duration of the mission. This is really only a concern during the first section playing as Arthur, where all four of you are progressing in firefights. Just be slow and aim first before firing. If you have any concerns that you may have accidentally shot an ally, reload the checkpoint immediately to erase the potential of it happening. After Arthur, Polina snipes and there is no chance of accidentally hitting an ally. Then it's Lucas, who is blowing up tanks and again there is virtually no chance of shooting an ally since they'll all be holding back while you destroy the tanks. Next is Wade, who pushes forward with the rest of your allies, but with Wade you should be using his Focus ability continually, meaning you'll be auto targetting enemies and not have to worry about shooting allies. Lastly is Arthur again, and your allies don't really move around in the firefight inside the hangar at the end, so the chances of you accidentally shooting one is really slim. The only real problem will be when the Jagermorder comes, and making sure you don't accidentally shoot an ally through the smoke. I actually just meleed the Jagermorder over and over to kill him, ensuring I didn't accidentally shoot an ally through all the chaos.

Unfortunately, there is no way to know for sure if you accidentally shot at ally during the mission and voided the achievement. If you finish the mission and this doesn't unlock, you'll need to play through the entire thing again.