Yagyū came from an average shinobi family and had a strong relationship with her younger sister Nozomi, who suddenly, without warning, died in a traffic accident. Yagyu was deeply hurt by the event and the solitude that came with it, but she knew (and feared) that over time, the loss of her sister would eventually fade from her memory.
As a means her never forgetting her younger sister, Yagyū dons an eyepatch crafted from her ribbon, cutting her vision and acting as a permanent reminder of her.
Upon her arrival at Hanzo Academy, she came across Hibari, who had such a striking resemblance to Nozomi that she had almost believed she had come back to her. Hibari's cheerful nature quickly overpowered Yagyū and the two quickly became friends. With Yagyū adopting an older sister role with her and seeing Hibari as her best friend that helped her get out of her solitude a little, she's always showing concern for her and being protective of her while also showing that she can't live without her, developing a "sister complex".
Although she will not admit it, Yagyū could never live in true solitude, and Hibari would soon become the primary reason she opens herself up to others, namely the rest of her class.
Hibari suggests Yagyu enter the "Super DIsh Gourmet Cook-Off" with her, but when Yagyu refuses until Hibari expresses disappointment and concern she couldn't do it on her own. Yagyu reconsiders and observes the flyer to find out the winner will gain a special scroll that will give them any wish they desire - deciding that her wish would go to becoming more friendly with Hibari.
However, she realizes if they both enter then she would possibly upset Hibari if they face each other. She quickly convinces herself not to worry over it though, since it'd only be a minor inconvenience and her wish would bring them closer anyway.
Yagyu comes across Asuka as her first opponent. Hearing that Yagyu is doing this for Hibari, Asuka claims to be jealous and wish she had a cute sister to share a close bond with. It's then Yagyu tells Asuka that she can be her older sister - surprising her. Yagyu insists that she is the older sister though and they momentarily act sisterly with one-another. Asuka compliments how well Yagyu fits the role and they quickly return their attention to the cook off.
Asuka is disappointed she lost to Yagyu, but she compliments her and makes her feel better before taking off. Yagyu starts to realize that she's actually better at cooking than she imagined, then decides that she enjoys portraying an older sister.
A bit later Yagyu finds Daidoji and is surprised when she speaks to her. She admits that she's always wished to have an older sister, and asks to play for a bit. Yagyu hesitantly agrees, only to see that Daidoji's idea of a game is a bit too rough for her after she kicks the object way too far from their location. Yagyu comforts her when she expresses disappointment and Yagyu brings up that they should probably resume the cook-off now.
Yagyu is surprised she won and Daidoji compliments her. They agree to share a mutual-sisterly relationship after realizing they both learned from the experience and Daidoji takes off. By this point Yagyu wonders if she should continue this or not.
Yagyu isn't surprised to be facing Hibari. Hibari notes that she doesn't seem very happy, and Yagyu confesses that she doesn't want to hurt Hibari if she would lose against her. Unfortunately, Hibari mistakes her comment and fears Yagyu doesn't think much of her as an opponent and starts to angrily chew her out.
After losing, Hibari starts to cry. Yagyu feels badly for this, but she cheers up really quick - happy that Yagyu just faced off against her with all of her strength instead of holding back. Hibari then asks that they celebrate her victory together.
The duo retire to a secret location and have some juice to celebrate Yagyu's win. Yagyu reveals to Hibari what happened earlier, and Hibari claims that she felt a little jealous of Asuka and Daidoji. Yagyu is surprised by her comment, but Hibari is quick to bring up the scroll and asks what she wished for. Yagyu hesitates, then realizes that she had gotten her wish already. Holding the scroll, she shreds it up and tells Hibari that her wish came true and its no longer necessary.
In the Senran Kagura anime drama CD, it appears Yagyū has a fear (or perhaps a phobia even) of theme park rides, in particular the Roller Coaster. This also is one of the times when her composure breaks.
Yagyū's name means "Willow Birth".
Yagyū's name and appearance are likely a reference to Yagyū Jūbei Mitsuyoshi, who is often depicted in popular culture as wearing an eyepatch made from the guard of a sword.
In Dead Or Alive 5 Last Round, Ayane dresses up like Yagyu as a DLC costume