To give an example of what I’m looking for, it'd be something like Angel's Last Mission: Love (think of her personality at the beginning).

Even better if the FL eventually becomes jealous and possessive too, but that isn't necessary as long as she has a bad personality and the ML is really sweet/positive in general.

Hmm, isn't this a typical trope in Korea?

Vagabond springs to mind (sorry that I've not watched a lot of Korean series).

For films, the last one I saw was Confidential Assignment (if that's the exact English translation.  It was a South Korean cop baby-sitting a North Korean military official on a mission the leaders of both nations want to keep hush-hush.  There isn't really a female lead, per se, but the sister-in-law who lives with the S.K. cop is absolutely gorgeous and is sooo damn rude to the him... but I think you really wanted romance in which the FL is horrible to the really nice ML, whom she eventually falls for?  (Which is, again, a very common trope).

^ I don't think it's that common, most of the (romantic) kdramas I see have a rude/cold ML and a FL who is strong and independent but with a sweet tone. What I'm looking for is the opposite; a FL with a bad personality (maybe she's even a bad person) and a soft ML who eventually understands why she acts that way and loves her regardless. Preferably tv series too, not movies.

Secret Garden comes to mind, the FL is quite cold towards the ML and irritated by him. (well both sometimes irritated by each other lol)

Another I watched recently is Full House, more of a cat/dog interaction though. I think the most fun scenarios I find is where the ML and FL have a cat and dog kinda relationship, I think that makes for funnier scenes and dialogue.

Another series is My love from the stars (aka. You who came from the stars), the FL is very obnoxious in the beginning towards the ML who is kinda just charming in his own cold way.

But I admit I'm having difficulty coming up with series where this is the specificially the case, usually this is flipped, the ML is cold towards FL.  

And as you mentioned, usually this is only in the beginning where the FL rejects the advancements of the ML, but eventually falls for him. I think pretty much every kdrama romance is like that :)

Okay so there are some dramas which are coming to my mind right now:-

1:- It's okay to not be okay ( FL is quite badass and also very possessive related to things and also gets jealous easily whereas the ML is very simple and emotional type)

2:- Itaewon Class ( Here you'll also see the strong character FL and innocent and sweet ML)

3:- Hotel de Luna ( FL is just awsm and you can see the bad personality of her and ML is quite and kinda easy)

Maybe:

  • Smile You
  • Game Sanaeha
  • Takane No Hana
  • Across the Ocean to See You
  • Dream High
  • Prosecutor Princess
  • Strongest Delivery Man
  • Page Turner
  • Happy Loner
  • Witch Yoohee

I know you're not after films, but My Sassy Girl is a classic, in case you've not seen it.

Sorry I couldn't help you out more.