This one was actually quite annoying
In order to get an A rank I have found the only things you need to do (really) are get an A rating on both rescue missions.
The first rescue mission is simple to get an A rating on. If you are on the last group of spiders, and ADA says "1 left", and all LEV's and buildings are intact, then go a blow up a building. You will get an A almost every time.
The second rescue mission is tricky: you need 9 to 10 LEV's to go down in order to earn an A rating. I would use Naked Jehuty, and simply hit the LEV's with the Halberd until they were in an SOS state. I had a good half of the LEV's down before I went on the offense with the enemies. And even doing that it was tricky to get the baddies to blow them up.
Time doesn't matter for an A rating - just the rescue missions. PLEASE NOTE
: Getting an S rating or higher on just 1 rescue mission, and an A on the other, will equate to an S rank post-game. You need to get an A rating on both OR a B and an S.
Questions, corrections and neg vote justifications in the comments below.