In order to gain a Overall Evaluation of B, all you need to do is three things:
1.) Start, and complete, the game on Hard
2.) Use continues 5 times (at least)
3.) Achieve an A Rank in all 5 rescue missions
Do not worry about things like time, enemies defeated, buildings destroyed (outside of rescue missions) - the above items are all you need for an B Ranking.
If you are having difficulty on Hard, I suggest grinding levels on the Factory mission immediately in the game. You can get to level 5 in ~40 minutes. After that it was smooth sailing for me.
This is very similar to the below trophy, with the exception of the continues required:
If you want to get this, as well as the above trophy, done in one playthrough, then after you beat the game continuing less than 5 times, load up your HUB.1 save (last missions), disarm all the bombs, and then let Zombie Neith beat you down a few times. Having her kill you means you will continue at the beginning of the battle with her as opposed to the entire level.
Once you have your 5 continues done, stomp her out fast and proceed to the endgame.
PLEASE NOTE: In order to get an A rank on the second Rescue mission you need to defeat Tempest (Boss #2) while doing slim to no damage in the town. My solution below for Tempest displays how to get that done:
If you have any questions, or throw me a neg vote, please enter them in the comments below.