Is it possible to get an 'S' rank?

Solution 1:

While I do not own the game, someone took the time to upload a set of videos where they play through chapter 1 on professional (so they have a bunch of things unlocked, making everything much easier).

If you look at these three videos, you can see them attain an S rank on that chapter, with relevant tips.

The important bit, though, is probably this:

While the above aren't necessarily the minimum criteria for an S rank, you will definitely attain one if you are at least that good (on that specific chapter, it obviously makes sense that the criteria are different for different chapters).