Ranks for now are purely determined by hits taken and time. If you go over 4 minutes it starts to subtract from the final rank, if you manage to do a mission under 2 minutes it should bump your rank up by one point. It's still possible to get an S-rank if you took one or two hits that way.
The 7th mission is very difficult with the amount of enemies and the close corridors combat, but I think if you use smoke bombs and spiders you might be able to avoid taking damage.