For those who haven't watched it, the FL grew up in a poor village where even her neighbors kills her dog and ate it because they were starving. And she wants revenge on her mother and father whom she thinks has abandoned her. She is outrageous, loud, and lacks all sorts of etiquette and is no better than any gossiping market woman, for lack of better comparison. But you still feel for her and realize she's a complex person and even though she's not likable you like her anyways. 

I guess I'm looking for a non-likable FL that's somehow likable :&

Link to the drama I'm talking about: https://mydramalist.com/736469-the-wild-duck, I seriously recommend watching it. It's a gem! :)

Maybe.....
Itaewon Class - ne of the female leads is just like you wrote.
Vincenzo
Miss Hammurabi
Our Time