This is your first "stealth" challenge - akin to the challenge maps in the original Batman: Arkham Asylum.
It will crop up about 20-25 minutes into the game as you search for the location of a gunshot (more details would be a spoiler).
Saving the medical volunteers is easy - there are four hostage takers to disarm and knock down, and you can do so quickly (within a minute or two) by swooping down behind them from the gargoyles up on high inside the building.
Just remain unseen and you'll get the achievement once all four hostage takers are downed.