She-Fu

The tendency of fight scenes involving an Extraordinarily Empowered Girl or Action Girl to also feature her doing impractical backflips, gratuitous somersaults, and gymnastic cartwheels to approach or evade her opponent.

Appears to be descended from "wuxia"-style martial arts action found in Hong Kong action films, though it may just be an excuse to show her body from every angle.

Examples

The New Batman Adventures: Batgirl (pictured above) was a skilled gymnast, and a girl in a skin-tight outfit, so she had this kind of fighting style.

Unlike her genetic father, Wolverine, X-23's fighting style is much more acrobatic and in many of her fight scenes she can be seen using flips and handstands to bring her foot claws into play. Justified since Laura is usually depicted as even smaller than Logan and very lightly-built, and since only her claws are laced with adamantium her body is much less durable.

In Iron Man 2, Black Widow uses over-the-top She Fu (and a dash of Lucha Libre) to clear the way to the Big Bad's computer system. In The Avengers, the character makes further user of She Fu to escape an interrogation, including seemingly disarming a henchman with her hair.

Yumi from Code Lyoko frequently uses such moves when fighting in the virtual world, thanks to her increased agility and the low gravity of Lyoko. Less so in the real world, though, where she sticks to more basic martial arts.

Samus Aran, especially in Super Smash Bros.. While she's in her Power Suit, though, she becomes considerably less acrobatic but gains an Arm Cannon with which to blast things.

Lili from Tekken fits this trope to a T. Has stylish balletic moves, with liberal use of flips. And a move where she does an aerial somersault; if she lands on the opponent's head, she does a double snap kick in the air. Take that, Reality!

The girls' throws in the Soul Calibur series tend to be like this, often putting their opponent between their legs.

Kasumi and Ayane in the Dead or Alive series.

The girls of Totally Spies!.

Wendy Wu, Homecoming Warrior on Disney Channel.

Amy Jo Johnson used to be a pro gymnast, so her character Kimberly from Mighty Morphin' Power Rangers naturally used She Fu in her fight scenes.

Yvonne Craig, who played Batgirl in Batman, was a trained ballerina. Batgirl's fighting style was heavily dance-influenced, with lots of spins and high kicks. Unlike Batman and Robin, she never threw or took a punch (though she would fairly often throw or wield an Improvised Weapon).