SAMURAI WARRIORS: Spirit of Sanada

S-ranks should come naturally but each battle is ranked on four criteria such as the following:

K.O.s
Time
Objectives Completed
Officers KO'd
Damage Sustained

The criteria are not the same for every mission: underneath the map, you can see what the criteria for S-ranks are by pressing twice in the pause menu until it cycles to them. In essence, aim to get many K.O.s, get hit as little as possible, try to take down every enemy officer and while doing this, try to beat the levels as fast as you can. You will likely earn this naturally while trying to complete all of the Multi-Stage Battle Objectives. Once you have received 10 S-ranks, the trophy will pop.

Note: Don't worry if you do not receive S-ranks and then proceed to the next chapter. Starting at Chapter 3, you can replay past battles in the Library in town.