You have to save all of these hostages in 1 playthrough, reloading the chapters after you completed the game will not work (reload the checkpoint if you fail to save a hostage). You will know when you need to save a hostage because there will be a small cut scene showing you the hostages and the enemies (with the exception of the 3 listed above). There are basically 2 different ways to do all of these hostage situations. Method 1, Gunz-a-Blazin! Method 2, Eye for an Eye!
Gunz-a-Blazin is to just kill all of the enemies as quickly as possible, starting with the guy or guys who are the biggest threat to the hostages. This works well when the enemies are bunched together and few in numbers.
Eye for an Eye just means, they have a hostage so you take a hostage. If your hostage is a superior officer over the other enemies, they will put their hands in the air and surrender. To check their ranks, hit . To grab a hostage, sneak up behind him and press .
If you mess up and a hostage dies, just immediately reload the last checkpoint. It tells you at the end of each chapter how many hostages you saved. Every hostage has an ID card, viewable in the start menu.
This will unlock in chapter 5 immediately after saving the single hostage in front of a very large yellow construction vehicle.
Notes on 3 hidden hostages
#1 - There is 1 hidden hostage on chapter 2. By hidden I mean, you will not get a cut scene or an objective for him and it will not show in the mission summary at the end. He's in a room on the bottom floor where you kick open the door and directly in front of you is an enemy looking at him. he's sitting against a pillar across from the door you come in. You have to go up to him and tap A to save him.
#2 - There is also a hostage on chapter 3, after you rescue the zoo keeper and he opens the gate. There will be 6 guys standing around him. You have to go up to him and hit A to save him but its not an objective.
#3 - And the final hidden hostage is on chapter 4 in the hospital. After you save the first hostage in the hospital, walk back through the door to this room and a guy comes stumbling through a door followed by an enemy. Kill the enemy and press A on the hostage to save him.