Family Tropes
Sibling Rivalry: Asami is the prime instigator, with her efforts to outshine her brother in something.
Denied Food As Punishment: Misako's preferred disciplinary measure.
Parental Favoritism: Expected to take care of her brother, the subversion comes when Asami realises that some of her issues are her own problems and not her brother's fault; her parents are reasonably handing out privileges and responsibilities with age. It makes her want this.
So Proud Of You: Her father thinks a handshake is as good as a hug.
When You Coming Home, Dad?: Her father works long hours.
General Tropes
All Women Love Shoes: Impulse purchases. They're cute and glamorous! Asami judges people by the shoes they wear. Extended in that her judgements apply to clothes and other manners of dress.
Schoolgirl Rival: Asami proclaims that Akane is worthy of being her rival, and will constantly engage her. She usually doesn't receive attention for her efforts.
Yamato Nadeshiko: A trope generally ascribed to people with traditional upbringings. Asami is described as having the looks and elegance of a Yamato Nadeshiko, and can pull off a pretty reliable impersonation when it's needed. However, she doesn't let her politeness get in the way of her being a touch passive-aggressive. This persona is a role she adopts as a way to cope with her home life and make herself appealing to gain attention.
Verbal Backspace: Asami says something. Then someone else says something or something happens that makes it clear that what she just said doesn't make sense. She quickly revises her statement and repeats it.
Afraid Of Needles: Nothing can unsettle her. Except for injections.
Cordon Bleugh Chef: Asami can cook well. She just bungs anything together without thinking if it works.
Combat Tropes
Battle Aura: Her Persona's unique skillset focuses around auras of varying effects.
Combat Aestheticist: Beautiful weapons and skills make a battle artistic. Subverted in that Asami's family home reflects this; there is a place for everything, and her father needs their familiarity and artistic merit to be comfortable - and her winning formula is the following.
There Is No Kill Like Overkill: All of Asami's tactics amount to drop a nuke on it.
Carry A Big Stick: Maces are her preferred armament