In order to get this achievement you need to go through the game completely non-lethal. This guide is not a step-by-step tutorial because I feel that these tips are easily enough to help you beat the game regardless of skill-level. The game isn't very long compared to Human Rev and doesn't offer many new challenges, so if you've beaten the last game this should all be obvious to you already. The first and most obvious tip is to SAVE. OFTEN.
You need to focus on using the following equipment:
-Pick-up Weapons: Tranquilliser Rifle, Stun Gun, Any weapon with EMP rounds (optional), EMP Mines.
-Augments: Energy Upgrade (VITAL), Hacking Tier Upgrade (VITAL), Jump Upgrade (VITAL), Tesla (optional), Glass Shield (optional), (Remote Hacking (optional and handy).
-Other items: Biocells, EMP Mines.
I went through the game using primarily Takedowns, the Stun Gun, TESLA, and the EMP10mm pistol (swapping between them but the first 3 all do the same job more or less).
Most Areas have obvious alternate paths (especially vents). If you get stuck in a situation where you cannot get past a guard/enemy because of their patrol path, use a throwable object to distract them, then move past. Another strategy is to use boxes to get to higher places rather than running in head first.
It is easiest to go through missions with as little takedowns (and evidence of your presence) as possible as there is less of a chance of patrolling enemies discovering your handiwork. Keep this in mind.
Helpful mission tips:
When you're first going to meet Koller you don't need to takedown any of the enemies. Also make sure you bribe/do the quest for the police officer on the second path leading to the Time Machine (Koller's place), as this will let you get past the guys at the front gate who can be a pain.
There are opportunities to use Biocells in certain missions to ease progress. If you are having trouble make sure to use them.
If you have plenty of Praxis kits and Biocells, upgrade Glass Shield to the max and you'll be able to fall back on it if you are about to be spotted.
DO NOT kill the vendor in Golem City that Otar wants you to kill (this unlocks a side quest-line so come back to this if this is your first playthrough).
In the GARM facility there is a large blue tunnel that can cut the area-time by a fair amount, keep an eye out for it.
In the boss fight with Marchenko, sneak around and locate the 3 security terminals which will let you disable all of his extra tech except for two of the flying drones. Make a save and test his patrol pattern. Then place an EMP mine where he is going to step, and then do a takedown.
I haven't tested this fully yet but I suggest not throwing knocked out NPC's off the map or using them as meat-shields. Obviously.
As far as I know there aren't any NPCs you need to save explicitly outside of the story to get this achievement. IE you don't need to quickly run here and stop NPC #857 from getting killed by a scripted event. Just don't kill anyone with your equipment/CQC/ etc and you should be fine.
If anyone has anything to add about specific parts in the game, feel free to write a comment. (If you still have questions, they may have been answered below!)