Don't forget the basics for Crystal Tower
For the crystal tower, the way it works is there will be 5 battles at first (each is associated with 3 to 4 FF games, and characters from those games will receive synergy - core characters will receive synergy for all fights). Note that if you use a character in one of those battles, he/she is unable to participate in the other four.
After you defeat all five battles, a 6th battle against Chaos will unlock. Note that you will only be able to use the 25 characters in the first 5 battles against Chaos. Note that initially only the classic version will be available, later on an elite version will be added, where the first 5 battles are in the D140 range, and Chaos is a 220 boss.