On the surface, she is much more mature than Kirito. However, dig deeper and she's a grade A psycho. Unlike Kirito, she "pretends" to care about people but probably cares about them less than he does.
Originally Kirito and Asuna were brief allies but when Kirito got his sweet ass coat Asuna wanted half of it which caused them to get into an argument. Kirito left and she began to hate him. Months later, they had to solve a (bogus) murder mystery together and Asuna ended up falling in love with Kirito. Asuna then began to stalk him and eventually forced him into a relationship and eventually marriage.
Because Hyde is the biggest enemy of Kirito, she wanted to kill Hyde for revenge for hurting him, however, she lost to him.
Ichigo is one of Kirito's friend. He wanted to rape Asuna but then he thought of the aftermath of raping her. He gave up and made friends with her.
Asuna thinks Reimu is cute and kind. Her cuteness makes Asuna want to make friend with her. She agreed.
Skodwarde killed her for Kirito mocking The BingBong gang.
Unlike Kirito. She does not like bullying you because you is the protagonist.
Because Kirito is the biggest enemy of The BingBong gang they sent out Skodwarde to kill her.