As the Description says Set 10 Hostages Free without triggering the execution timer. You also need to make sure the hostage gets to extraction.
The Ideal method is to be as stealthy as possible, and not let the Guards or Cameras see or hear you.
Most Prison maps will usually have at least 1 stealthy route available, usually via an Airvent of some type. I recommend getting yourself familiar with the prison maps.
Stealth Warframes such as Loki are ideal to earn this, but not required.
Silent Weapons, such as Bows and Kunai, can help, as with a stack of Auto hacking tools.
As only one member of the team needs to break in, you hide outside while stealth expert breaks the hostage out.
Due to the way that most alternate routes are open on Earth and Venus maps, I recommend farming on these two planets.
(I earned this achievement with Mag, Excalibur, Trinity, Rhino and unranked Mirage. None of them are were set up for Stealth.)