Pretty much as title says with female mc Something like snow queen couple or trouble take care of the lady nice guy I would like a respectable cool guy to change the girl and have the girl falling for them unintentionally I would like a slow romance and change with the female mc
I haven't watched a lot of dramas like that but on all those dramas I watched, Prosecutor Princess fits about 1/2 of your description. The female lead is not really a mean crazy female dog, although she is a bit insensitive and shopaholic.
Witch Yoo Hee Me Too, Flower I Do, I Do Kimi wa Petto Bad Couple (it's so-so) Tough/independent (sometimes self-centered) women: King2Hearts (Not a beyotch, but tough/independent) The Woman Who Still Wants to Marry (Not mean/crazy - but career driven, independent) Faith
Since you don't have anything listed not sure what you have seen so these are ones I think fit and I liked - That winter the wind blows Greatest love Missing you Dream high Protect the boss I love lee tae ri