The game is vaguely megaman-ish - if you looks at your skills you'll see a little graph at the bottom of the pop-up that shows the girls' faces on a graph. It's showing you which girl that skill is most effective against.
SIlence is basically weak to everyone but Labyrinth; she's absolutely meant to be the easiest girl to defeat. Arnesta is weak to Silence; Citron is weak to Arnesta; Labyrinth is weak to the secret boss; Aquila is weak to Labyrinth, and the secret boss is weak to Labyrinth and your starting skills.
Checking my deck against Citron, I'm loaded up on Acid Rain (short cast time, lots of zone control) and Noble Cross (which she's weak to).
Citron is absolutely meant to be a bitch of an opponent on your first playthrough. I don't think I actually got around to beating her until my third playthrough. I played this a shit-ton when this came out, as a direct result of FFXIV Endwalker having an incredibly scuffed launch. Heh.