First Plague Wall you encounter will be at the Crashed Plane Site with Logan and you are tasked to destroy it but may also fail if you run out of Plague Buster.
When I say fail, I mean that you will move on and walk away from the Plague Wall and recruit Logan, you can come back later when you have more Plague Busters to finish off what you have started.
Every Plague Wall requires three Plague Busters and a third of its' health removed by Lethal force. Every time a third of the Wall's health is down, it will cover itself up and you will need to throw another Buster and use lethal force to kill it.
This can also be obtained if you assisted someone during a Plague Wall attack.
There is another achievement similar to this one where you must destroy 20 Plague Walls