You can rank up the characters by collecting enough Cores (fragments) of that specific Fatima, and then tapping on the "Rank Up" button (you can find this in Fatima - AI tab). There you will also see how many Cores of that character you currently own. The characters will start at C Rank, and with enough Cores (you will need 10 for start) you can rank them up to B Rank. Once they are B rank, you will need more Cores to rank them to A Rank. After A Rank comes S Rank and S+ Rank, which is the highest. It will take a little to get there, but in time - everything's possible.