To get a higher rank in a battle, make sure that the final move you use in that battle is Ledah's Over Skill called "Lost Seraph". If done correctly, Ledah will say "Pay for your sins with death" and you should get a higher rank. For example, assume that there are three enemies. Kill two of them and have one remaining. Lower the final enemy's HP down enough for Ledah to finish him off with Lost Seraph. The battle will end and Ledah should say "Pay for your sins with death". You should now have a higher score and a rank.