This is pretty straightforward. First, save often and reload if you're unsure. Second, you can sneak by a few cameras and a robot in the entrance area with a little patience. Third, once you get into the main vault area, if you hack both level 3 security terminals (use multi-tools if you want to), and you upgrade your hacking to include both robots and turrets, you can pretty much turn everything off in this area and have your free run of the place without having to worry about being detected. Other than a few turrets hidden inside some of the secondary vaults (none of which you have to enter), there is nothing else that will prevent you from getting this achievement, which unlocks around when you get to the mainframe.