You must get an S rank on 3/20 DIFFERENT levels, not 3 on your favorite level (1 for each difficulty).
The Circle of Lotus (on Hard) - 60 Combo. 59 seconds. 3259 points.
I received my first "S" rank fighting Master Mo in Level 8 on Hard. Once you get the hang of the fight it is surprisingly simple, just hold until he does one of his attacks; one of which is a pull back and punch forward attack where he spins his arms around as he moves back, you only need to tap once for that. Another one is a sort of arm helicopter where he'll wind up briefly and then start spinning into the air, just keep tapping for that one. He does another forward punch similar his first move, but without the arm spinning, which is probably his quickest and least used move. Finally, he will use a ground stomp AoE that you MUST dodge by pulling the when you see the ! over his head. Once he reaches 50-60% hp and he spawn 2 black circles on the ground that you cannot stop in, otherwise he'll kick the crap out of you, so keep comboing him up by holding and jumping over him when one of the circles comes to close. The entire duration of the fight, be sure to HOLD and when you can use your Chi attack, especially when he is about to attack (his first attack and AoE attack are great places to use this.).
Sword Pair (on Easy) - 3104 points.
This is the second level in the ninja section of the game, and will take place on a rooftop where you must find wave after wave of ninjas (including clones of the ninja boss you killed a few levels ago). I did this on Easy, and all you really need to do on that difficulty is keep attacking and whenever you see a volley of shurikens/throwing knives coming toward you, spam to deflect them back at the ninjas. All of the harder enemies, the ones with healthbars, are VERY easily elimated with a critical hit, which was also incredibly easy for me to get (maybe luck), and each critical hit one shot every one of the enemies with health bars at the top of the screen aside from the ninja boss clones at the end of the level, which took two shots (they stood in a group once they split so I hit all 4 of them at once.) If you have trouble on this, get some deflection skills, or just simply practice the level a bit, it's pretty straightforward and really just a button mashing fest.
Break (on Hard) - 3568 pts, 2 Crits, 150 combo, 1 min, 0 damage. (Either Time or Damage are key)
This one took quite a bit of practice to perfect but some things to note is that you want to absolutely UNLOAD on the Monk boss you fight at the beginning of the level. Hold nonstop and once an pops up over his head be ready to tap , since that is generally what follows and missing that can cost you time and health. If you manage to stun him (stars over his head), he often comes out of this and goes straight into one of his power attacks, one being an almost immediate uppercut that will most likely deal damage to you, and the other is a slower attack that you can beat with your Chi or just block/dodge (Chi=time saver). After some practice you should down him in one single combo.
Once he is dead, 4 regular monks will spawn on either side of the area to fight you, immediately grab the horn the boss monk dropped (if it didn't drop, you may be out of luck time wise) and immediately summon your most powerful ally, shut off your weaker ones prior to battle if necessary. In my last few attempts I was lucky enough to have the super epic Swordsman ally, which I got from this level while trying for this S rank, and he dominated 2-3 of the monks each time.
After watching how my stats change the score it seems that time > damage > combo in order of importance, I'm not sure how critical stacked up but I generally only got one during the level so that may have helped too. Flow like water and you should have this in no time.