So I'm looking for dramas where the female lead is either plotting and seeking revenge, redeeming her past grave mistakes, taking/restoring back her rights, saving the company/nation/kingdom, etc. The point is, she is doing some kind of ultimate mission. Her conviction and determination in doing this 'mission' is so strong to the point she would do whatever it takes to accomplish it, no matter how ruthless or immoral she becomes. I don't want her to stay pure and benevolent, but it's okay if she's only ruthless to her enemies and kind to her friends. At the same time she's also suffering inside, maybe because of bygone regrets, grieving for her loved ones, moral dilemma, not wanting to be the kind of person she has became, etc. I would really appreciate it if not only it has what I'm looking for, but it also has good plot and characterization and acting. Some romance would be a nice ingredient but not really necessary. I can take tragic or open ending. Thank you~
I can recommend K-drama Golden Empire :)
Myung Wol the Spy possibly.

I usually watch weak females who get taken for a ride so this is hard for me.
You're looking for this drama : http://mydramalist.com/621-byakuyako
This is exactly it. It's dark, the female lead is wronged and seek revenge, helped with the male lead, no matter the cost. 
Alos, Empress Ki http://mydramalist.com/7114-empress-ki

Girl have to fend for herself from a young age, is eventually sold to slavery to another country because of an injustice and plans her revenge. Eventually manipulate her way into the Emperor's heart (whom she first hates) and climbs the steps of power until she can catch the real bad guys and end them
I second  @Juniko 's recommendations... as for Byakuyako (2006) ... BUT, I suggest watching the movie versions first, else the suspense will be ruined.

J-movie -- Into the White Night  (2011)
K-movie -- White Night (2009)

I also suggest DO NOT read the synopsis for the drama Byakuyako ... imo, it ruins the suspense since it is gives SPOILERS!!!
Instead, read synopsis for both movies.
sounds like you need some Empress Ki. I saw that you dropped it at the third episode but if you're looking for a major awesome ruthless female lead, you should definitely consider picking it back up again. She was cool in the beginning but she gets waaaay more awesome later on. 

here are some other dramas you might like:

Heaven's Promise (so I know this one is really long but it was definitely worth the watch. The first 50 episodes are so are just about her getting stepped on really but it builds the foundation for the whole revenge plot and when she comes back she becomes really awesome and revenge never tasted sweeter)

return of the heiress (in the beginning she was pretty naive and easily manipulated but she wisens up really fast and becomes a force to be reckoned with)

one well-raised daughter (another really long one but worth the watch. It was a lot deeper and dark than the synopsis hints at which was a pleasant surprise) 

on another note, if you're looking for a ruthless and immoral character that isn't your typical Kdrama heroine you might try Miss Ripley. It doesn't necessarily involve a revenge plot but the female lead was very unique and the complete opposite of the stereotypical pure naive heroine. 
The K2 sounds like it's going to be like this; it starts airing September 23rd.
hwang jin yi

empress ki

jang ok jung

temptation of wife
Queen of ambition she is ruthless and immoral. This is an awesome revenge drama, however she is not the one seeking revenge.
Monster (2016) is the only one I can think of. It has 50 episodes but has the characteristics that you have listed. It drags sometimes but overall good. It isn't only the female lead that seeks revenge because the whole kdrama revolves around revenge
Temptation of an Angel Kdrama fits this description perfectly.

I think the negative reviews just have to do with individual opinion not the show itself, when I read your description this drama
came to mind immediately. Strong but tormented female lead that you kinda understand why she's like that and she's not just
simply evil but on a mission however unfortunate for all.

Interesting twist towards the end too.

Ha, those are my favorite types of dramas and I really wish they would male more of them! 

Angry Mom and Dong Yi. They don't exactly fit in that they stay "pure" in terms of character (especially DY), but I would say they do a fair bit of plotting and they do have ultimate missions. Give 'em a shot! 
I think Bachelor's Vegetable Store fits all your criteria.  it's a weird drama, almost every time someone specifies a criteria it fits (which might give you some indication of it's nature), I find myself recommending it much more than it deserves.  I mean, it's fine.