Getting the S rank in Raid mode seems almost entirely dependent on one factor - the amount of damage taken. Trying to get a solo no damage bonus at or around the recommended levels can be very frustrating, so the easiest way to get an S rank is simply to come back once you are at a much higher level and blitz through the stage. Not only will you have plenty of decent weapons and mods, but beating enemies so easily will help with your accuracy and completion times.
For the chasm levels that I hadn't already got an S rank for, I went back with Jill along with a rapid fire machine gun, rifle and lightweight handgun. With this combination it was possible to blow through the stages very quickly, picking up an S rank every time.
The important thing to remember is that it doesn't have to be a perfect run, you can take a few hits and even use a herb (needing more than 1 seems to give you an A rank though). You don't have to kill every enemy, so just run past those you don't need to fight. Grenades are very useful as well - decoys for the oozes, electric for anything in the water and those big running turtle things, pulse for the invisible hunters.