Many of the solutions here have invaluable information and help when it comes to the daunting task of S-Ranking this game. However, the math really isn't there, and there's a notion that keeps popping up that has been bugging me.
A lot of the solutions for the 4 S-Rank achievements emphasize finding red orbs to help boost your success and that its integral to acquiring a high rank.
While collecting orbs is fine and dandy, STYLE is your key factor in S-Ranking this game on ANY difficulty. The fine posters at gamefaqs have deduced the ranking formula to help you approach a level from a mathematical standpoint and figure out how well you need to perform. The full guide (with ranking information straight from Capcom) can be found at: http://www.gamefaqs.com/xbox360/938686-devil-may-cry-4/faqs/...
(Clear Bonus + Stylish Points) x Clear Time Multiplier x Difficulty Multiplier x Orbs Found Multiplier x Bonus and Penalty Multipliers = Devil Hunter Points
Every level has a base clear score, and that is added on to your stylish points. EVERYTHING ELSE IS A MULTIPLIER. A fast clear time with every single orb found won't do you shit if you don't have the style to back it up. Don't get me wrong, they definitely help, but your main focus should be comboing, variety, and getting hit as little as possible. Not getting hit is ideal, as that adds another multiplier, but in reality, most people going for these achievements aren't gonna get perfect runs.
CLEAR TIME MULTIPLIER
Obviously one that gets focused on heavily, your clear time ranking has a heavy influence on your Devil Hunter score as it has the potential for the highest multiplier. If there is any factor you want to S rank consistently, its the time. The multipliers are as follows:
S = x3.0
A = x2.5
B = x2.0
C = x1.5
D = x1.0
Getting an A rank on time isn't the end of the world, but you have to have the style to back it up. If you're having a kick-ass style run, tho, getting an S-Rank on clear time shouldn't be an issue.
The other factor that gets given tons of attention, the orbs multiplier is the other rank based multiplier of the formula. People seem to think getting an S is mandatory, especially on Human due to a "lack of enemies to get style points." This is entirely NOT TRUE. An A rank is entirely sufficient on ANY difficulty, and here are the multipliers to show you why:
95-100% --> S = x2.00
75-94% --> A = x1.75
60-74% --> B = x1.50
45-59% --> C = x1.25
0-44% --> D = x1.00
See that? The drop from S to A is NOWHERE near as drastic as the drop on Clear Time. Yet another upside is an A only requires 75% of the orbs, a much less daunting task than the 95% needed for S.
This, again, is not to say you should skip searching for Red Orbs. It just means you don't have to fret if you think you missed those 2 or 3 chairs in that one room. Having knowledge of where secret locations of Red Orbs are is a great way to ensure you get an A, and if there is a Combo Adjudicator or a Red Orb stone in the level, abuse it to all hell.
BONUS & PENALTY MULTIPLIERS:
These are the little "awards" that are displayed underneath your 3 ranked attributes. Most of the time people see No Item, here, but there are actually quite a few modifiers that can show. Unfortunately, most aren't as good as we'd hope:
No Damage = x1.5
No Item = x1.2
Continues = x0.8
Enemy Handicap = x0.8
Gold Orbs = x0.7
Super Character = x0.2
Obviously having a perfect run of a level would be fantastic. If you can do it, good on ya and have fun pretty much ensuring an S rank. These multiplier mainly apply the most basic common sense if you're going for an S rank: don't use a super character and DON'T DIE.
Ever notice how everyone talks about how you get more Proud Souls for playing on DMD? Well that's because the amount of Proud Souls you get is based on your Devil Hunter Score, and your Devil Hunter Score is multiplied by these factors depending on what difficulty you play on:
Human = x0.85
Devil Hunter = x1.0
Son of Sparda = x1.8
Dante Must Die = x3.0
[NOTE: These numbers are not 100% accurate and from Capcom, but have been deduced by the folks at gamefaqs and they are pretty damn close. Like, within 2 or 3 points of Devil Hunter Score close. So it shouldn't be anything to worry about.]
FIGURING OUT HOW AWESOME YOU NEED TO BE FOR AN S-RANK
OK, we know all those fancy schmancy numbers but how is that going to help us? Well we just solve for x, with x being STYLISH POINTS. That there is your main concern and will make or break your S-Rank runs.
Take a step back and think about how good you are at the game. Contemplate how you think you will rank on time and orbs. Contemplate how much ass you are gonna kick and how much your ass is going to get handed to you. Think about these factors realistically.
Then, approach the formula. Look at the level you want to S-Rank, and find its Devil Hunter Score on your difficulty in the guide linked. Let's take Level 3 on Human for an example. 55250 Devil Hunter Score is the cutoff for S-Rank.
Again, base this off your own knowledge of how well you play, but for this example I'll use my expectations. For me, an S on time is mandatory. In all honesty, it should be for everyone, but if you want to aim for an A, aim for an A, it's your perogative. An A on orbs is generally my goal, but I know sometimes I'll only get a B, so I calculate for both. I'm not going to die, so I can ignore the bad bonuses, and I know I'm going to get hit, so the only bonus I factor is No Item.
The clear score for Level 3 is 2000, so our formula becomes:
(2000+x)*3*(1.75 or 1.5)*1.2*0.85=55250
Using basic algebra, solving for x gives me 8318 for an A on orbs and 10037 for a B on orbs. I HAVE to get over 8318 stylish points, but I intend to get more for security.
As has been said, beating a level on a difficulty will have the stylish points be displayed on any replay. Use that to gauge how well you're kicking ass and whether or not you're gonna be starting over. Stylish Points go up faster the higher your rank. Getting hit lowers the rank, so please, get hit as little as possible to save you some trouble.
This is a lot of info to absorb, but using this formula will make it easier to give you a goal to aim for on ANY difficulty for this game. These achievements are hard, and they WILL test your skill and patience.
Good luck to all of you.