One characteristic is their independence. For example, in 'The Handmaid's Tale', Offred, though in a very restricted and oppressive society, still tries to hold on to her sense of self and make small acts of resistance, showing her inner independence.
Badass female characters in romance novels are often independent. They don't rely on others to solve their problems. For example, in 'A Court of Mist and Fury', Feyre is able to make her own decisions and stand up for herself. They are also brave, like Jude in 'The Cruel Prince' who isn't afraid to face the dangerous faeries. Another characteristic is that they have their own goals. In 'Red Queen', Mare wants to change the world for the Reds, and she doesn't let her romantic feelings completely overshadow this goal.
In these fics, Sakura often becomes badass through intense training. She realizes that she needs to be stronger to change things in Konoha or to prove herself. For example, she might train under a mysterious master or in isolation, like in 'Sakura's Solitary Training' where she spends months alone in the forest, honing her skills.
One great 'badass female romance novel' is 'A Court of Thorns and Roses' by Sarah J. Maas. The female lead, Feyre, is a strong and capable hunter who gets drawn into a magical world. Another is 'The Cruel Prince' by Holly Black. Jude, the main character, is a mortal in a faerie world and she has to fight and scheme her way through various challenges while also having a complex romantic relationship. Then there's 'Red Queen' by Victoria Aveyard. Mare Barrow is a poor Red girl who discovers she has powers in a world divided by blood color and she has a passionate and tumultuous relationship journey.
Well, it could be characters like Draco Malfoy. In the original series, he had his moments of growth and in fanfics, he might be one of the main Slytherins to defend Hogwarts. Maybe he finally realizes the importance of the school and his own values change. He could be joined by other Slytherins who were perhaps overlooked in the official story but show their true courage in the fanfic.
In some fanfictions, Snape has badass moments when he outsmarts Voldemort. For example, he manages to mislead Voldemort about the location of a crucial magical artifact. He uses his Occlumency skills to his advantage, hiding his true thoughts and intentions while presenting false information in a very clever way. This not only shows his intelligence but also his courage as he risks his life to deceive the Dark Lord.
His attitude. Percy in fanfiction often has a 'don't mess with me' attitude. He doesn't shy away from a fight and is always ready to stand up for what he believes in. He'll face any opponent, no matter how powerful, without hesitation.
His unwavering determination is another factor. No matter how tough the situation is, Adrien in fanfictions doesn't give up. He is willing to risk everything to protect the people he loves and the city he lives in. This strong will and selfless attitude are what make him a truly badass character in many fanfictions.