*From Xbox Achievements*
In each carrier stage, survivors will be taking shelter in certain buildings; 'rescuing' them requires destroying the buildings that they're in. This achievement requires you to rescue all survivors in all 20 carrier stages. You'll unlock this naturally as you work towards the "Renegade Dismantler Corps" which requires the destruction of all buildings in all carrier stages, as survivors are found only in buildings.
Importantly, the first time that you attempt each stage, focus on clearing the carrier's path above any other objective. Once you've done this successfully, you can re-enter the stage at will in a free-roaming mode, without any pressure from the carrier's progress, or indeed any time limit at all - and this is the best time to go for a full clear of the stage.