In order to gain an A Rank on any rescue mission you need to complete the following:
1.) Prevent less than 10% of the buildings to be destroyed
2.) Save
EVERYONEI found that the first 2 rescue missions were the most difficult, not because of any lack of understanding regarding gameplay mechanics (i.e. the standard learning curve that comes with most games) but rather the areas you needed to save.
Rescue Missions appear after certain events in the game, so if you are looking for a Rescue Mission and you don't see one, chances are you haven't progressed far enough in the story. You will know when they pop up in an area: that area is outlined red and there is a nice "SOS" sign on it (as well as a flashing SOS sign on your display

).
RESCUE MISSION 1Location: TOWN.2Here there are about 6 squads of mostly Raptors and Mummyheads. The Mummyheads are far less annoying than the Raptors here. You need to not only get all the Raptors attention, but you need to lure them to one of the two corners on the map free of buildings they can hit.
Your best bet is to get everyone's attention as quickly as possible, so they are focused on you instead of buildings, and take them out all at once.
RESCUE MISSION 2Location: TOWN.1Worst one in my opinion, simply because if you were not careful during the Tempest fight, and made a mess, it counts against you here

. Refer to my solution below for more details:
Once again, you have Raptors and Mummyheads here, but they have been joined by several Cyclops as well. Once again, getting as many squads attention and luring them into the culvert in the middle of the map worked the best for me. I did leave one group at the other end of the map alone since its patrol did not really give it much (if anything) to destroy. I saved them for last

.
RESCUE MISSION 3Location: TOWN.3Personally, this rescue mission was not what I was expecting. I think it started with 9 or 10 squads, but most of them do not move at all. Here I would advise going after the groups that do move, and saving the stationary guys for last.
There is also another culvert here where you can dispatch enemies without worrying about people or buildings.
Once again, the guys you are dealing with are Raptors, Mummyheads and Cyclops.
RESCUE MISSION 4Location: CITY.2After you get infected during the Tyrant sequence, get out of the Park ASAP. You will be infected with a nasty virus that keeps your health at 0.01, making you susceptible to anything, and everything. You will also see a rescue mission pop up on the screen.
DO THE RESCUE MISSION. I can not stress this enough. If you try to fix yourself first, you will lose the A Rank. Period.
Do not worry about this rescue mission - it is literally the easiest one in the game. All the survivors are in helicopters, and you have 3 squads roaming around: 1 squad of 2 Raptors, 1 squad of 2 Mummyheads and 1 squad of 1 Cyclops. Best part: they are all seriously low levels.
By now you should be relatively familiar with the game mechanics, so this will be a walk in the park. Just remember, the survivors are mobile in helicopters, and they can (and will if you are not paying attention) fly in front of you talking a bullet intended for an enemy, so be cautious of the distance you keep from the enemies in combat.
RESCUE MISSION 5Location: CITY.1This is where you knocked down the spinning column during the EPS missions - now, apparently their are survivors in the supports

.
This mission is not too bad, as you will notice no enemies are really even firing at a structure or people. HOWEVER, once you engage them, they turn into asshats and start shooting the crap out of all the stuff you don't want them shooting!

Once again, you have your standard squads of Raptors, Mummyheads and Cyclops to take care of here. Focus on one group at a time here, and take your time. Try to stay on the outer edge of the map to keep enemies from running back to the center shooting everything you want to save.
If you want me to go into more detail regarding a specific mission, please ask in the comments below.