S ranks in mission mode are the same as the Story in the sense that you are graded on soul points earned in battle, time, difficulty, ignition attacks and number of foes defeated. When going for the rank S more often than not you can disregard the time bonus as you'll want to focus on eliminating as many enemies as possible, all the while getting your slash counter up. That said, you'll want to use a high leveled character with each of combo enhancement nodes unlocked so your slash meter depletes as slowly as possible.
Depending on your style, you may also want to spam ignitions but if you feel having the enhanced state will keep the combo going you'll want to continue with that. Constant multipliers beats the hundred or so points you get. Most of the time I would get my S rank while playing on hard so there was less to worry about clearing each of the missions on very hard, again, it's all depending on how you want to approach the game.
Good characters to use to accumulate S ranks are Uryu with his jump circle move, Ichigo with his standard Square x 4 combo into his jumping circle repeatedly. This fills your ignition gauge as well as ups your number of slashes fairly nicely. Barragan is also a good option, however I haven't used him much personally.
You must get an A rank on the first 27 missions to unlock the final mission regardless, so you may as well get all of your S ranks while you're at it. If there's anything you'd like to see improved upon, feel free to comment.