I don't know if I'm remembering this correctly but, I think it was pretty new, about a girl who learned how to fight from books or TV, and goes around beating up people who owes her mother money, because her mother is poor, sick or dead (I really don't remember ;_, and that ends up leading her to her dad, who is connected to the Yakuza?

Any help at all is greatly appreciated!

I doubt this is the one but it has some similarities: Show Me the Money

At the beginning the protagonist is actually a guy but the main girl is a more interesting character and her background have a greater part in the story. She is super strong, and totally crazy when it comes to money (but for a noble purpose - as is customary in these stories). She pays the medical bills of someone she calls her sister, who's been in a coma for 2 years. Also, the first time she meets her step father (who is a bit shady at the time), the protagonist thinks she is working as an escort to make even more money.
Well, it's probably not correct but...

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"The light shines in the darkness, and the darkness has not overcome it."

I remember now...it was a movie, not a manga. my memory is so terrible..

Its from the Thai movie Chocolate as i remember

Woot that's it! Thank you!