DMC3 Rank Evaluation is much more complex than it's previous predecessor. Because the crtierias for each missions varies on each categories including the diffculities. For example:
Therefore, some difficulties requirement including the respective rank will be unknwon and require data gathering/testing from the game itself. Furthermore, this game has SS Rank which is the Rank players get when they receive an S at the end of mission Results screen in all of the following 5 categories; Time, Orbs, Style, Damage, and Items.
isn't displayed until you go into the Total Rankings screen.
The higher the difficulty, the stricter the requirements are. As a result, the most challenging task to take on in DMC3 that's documented in the game is completing Dante/Vergil Must Die mode with SS Ranks.
(Total Time that Style Meter is Empty + Total time current Style Meter × Style Rank) × (1,000 / Total Time). Time spent outside of battle does not count.