Call of Duty Advanced Warfare Not on my Watch Achievement/Trophy will give you one Bronze Trophy or 10 GamerScore points depending upon your console. In Induction mission, you have to protect the walking tank and not let it get destroyed by the Drone Swarm.
To get the Call of Duty Advanced Warfare Not on my Watch Achievement / Trophy go to the street with a high-tech tank on the left side in Mission 1: Induction, you will get to this street quite early in the mission.
Suddenly a huge Drone Swarm will be attacking the tank, get into the turret which will be at the far end of the road (objective). With the help of the turret’s EMP, which will take about 30 seconds to start, keep shooting the Drone Swarm until its down.
If you are still unsure, check out this achievement video given below: