To obtain Player rank S you will have to:
-Obtaining rank S in strory mission:
The rank you will get depend on how much cash you earned on mission, you can improved the outcome by completing subquest, doesn't losing much AP, using thermal weapons (avoid using chemical weapons, those are most expensive!), most missions got subquest; no damage and time limit.
-Completing subquest in story mission:
The subquest could be many thing; no damage, time limit, scrap collection, destoying more units than friendly AC, fast destruction etc...
You can get it by just playing story mode.