For all the SSS grades on all the stages, I would recommend taunting right at the beginning of the stages for every 1-3 guys you kill. That'll get your style meter up to S very quickly, and then the rest of it is just not getting hit at all throughout the stage, and not letting too much time pass between kills and/or damage done to bosses.
Also, definitely try to make it through the stage quickly, but there's no need to frantically speed your way through. Lastly, I'd recommend going for these grades on Easy Story Mode, but I got plenty of SSS grades as I went through arcade mode. You might not even need to go out of your way for these all that much.
Good luck, and keep at it! You can do this!