This takes place in the level, "Archives."
Playing along, you will eventually get to a large room where you will see many large black electronic boxes. These are the servers.
As an extra hint, the eye signifying an objective needs to be done will begin flashing in the lower right hand corner of the screen.
The tricky part here is that they are all not in the large room; facing the main objective, on the left hand side there will be a closed room. You will need to climb through a vent on the right hand side of this room to access it.
Alright, now that we've located the servers, here comes the fun part.
How I got it was with my pistol, and two automatic weapons. Starting in that side room, use your pistol to destroy what you can. From there, begin to make rows down the servers. When you have to reload, switch to your next weapon. After all three weapons need to be reloaded, just wait for your automatic weapon to reload, then keep on firing. Try to find a route that works with you.
Obviously, it helps to kill all the guards before attempting this, careful to not accidentally destroy a server in the process.
Lastly, reloading to last checkpoint if (or when) you screw up the achievement will NOT affect it. You can do this as many times as you like.
If you downvoted this solution, tell me why so I can fix it.