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This achievement will require that you complete an entire playthrough without ever having raised a single alarm. As mentioned above, this is best stacked during a playthrough where you're going for the "Pacifist" achievement. This works best since you will be bypassing enemy encounters stealthily, thereby reducing the chances of ever being seen. If you do happen to accidentally raise an alarm, you can reload your latest save and carry on.

Please be aware that enemies can become suspicious and enter the "search" state. The achievement will not be void until an actual alarm is triggered and the enemy goes from "Search -> Hostile." You can also loosely keep track of this by keeping an eye out for the "Ghost" or "Smooth Operator" bonuses after completing an objective/mission.

NOTE: These bonuses will not always appear even if you do remain completely unseen and do not raise any alarms. This is because some sections of a mission do not have alarms. It's tough to rely solely on the presence of these bonuses to track progress, so just make sure you are reloading your latest saves if an enemy becomes hostile.

Thanks to PowerPyx, you can follow the guidelines below for actions that trigger alarms and actions that must be avoided:

Running into red laser grid
Failed Hacks (Timer reaches 0:00 and/or Access Point is traced)
Always back out of the hack before time runs out or you are traced. You can reload a save if this happens, though.
Enemy activates Alarm Panel
Enemy finds someone's body, then goes on to trigger an alarm
Security camera finds a body
Shooting security camera and/or security robots
Security cameras going full red
Turrets going full red and shooting at you
At the start of Mission 13, G.A.R.M., you must call Vega, not Miller. Calling Miller will cause an unavoidable alarm in the first enemy section of this mission.
Do not use the drill (skip the "Core Driller" achievement) and do not take out any enemies in the first hall. To get to the next area go through the electrified pipe in the north-east corner of the hall instead of using the keypad at the door.
In Mission 15 you must do the optional objective "Neutralize All Enemies in the CSO 11/11."
If you don't do this, the reception area of Mission 16 will be hostile and have an alarm.
Lastly, it is highly recommended to focus on unlocking and fully upgrading the following augmentations for this playthrough: Glass-Shield Cloaking, Smart Vision, Hacking Capture, Hacking Stealth, Cybernetic Leg Prosthesis, Icarus Landing, Cybernetic Arm Prosthesis, Wayfinder Radar System, LiDar Mark-Tracker, and Sarif Series 8 Energy Converter.