I am not that good, some people have done SS for all of the difficulty levels, up to Dante Must Die... that is hard!
On mission 2 when you are trying to get SS, what rankings are you getting for time, style, orbs, damage and items? The most important things about succeeding all fit together (in order of priority)
1) Avoid getting hit by jumping or rolling or dodging
2) Continually hit enemies when you get the chance
3) Keep changing the attacks you are using, so you get more style (if you use the same move over and over, you won't get as much style bonus)
4) Don't kill enemies until you are up on the style meter. You get more orbs for killing an enemy when you have high style. So if an enemy is close to dying, but you are only on B, leave them for the time being and go to another enemy to get more style, then you can get A or S for both enemies.
5) Taunt whenever possible. This gives you extra style for free. Especially good just after killing an enemy, as it boosts your style while there is a gap before you fight the next enemy
6) Use the DT charge move (hold L1, and wait for your devil bar to fill then release). This will do lots of damage to surrounding enemies, and can kill an entire horde if you've done them a bit of damage beforehand. You will get your style full right up, and get full orbs from those enemies.
So, all those things work together to help you get SS ranks... If you avoid getting hit, then you will stay on your feet and get the levels done quicker. Also your style will remain higher, because style drops whenever you get hit. So if you maintain a high style, you will also get more orbs. Avoiding getting hit also means you won't take damage, and therefore won't need to use items. By taunting you get more DT bar, which you can then use to do the DT release, which kills everyone super quick and gets more orbs!