You seem to have the right idea of how to do research: Read/watch as widely as possible, concentrating on works created by people from Korea, and including material from outside your comfort zone. Even soap operas may be useful, if you want an exaggerated sample of everyday life.
Some other things to consider:
How familiar is the character with your own culture?
Suppose your home city is Paris. Writing a Korean who has lived in Paris for the last 20 years will be easier than one who lives in Seoul. A young, urban Korean will be easier than an elderly Korean who has always lived in the same remote village. And so on.
How prominent is the character in your story?
Does the Korean character only appear for a few scenes? Is she the major antagonist, love interest, or sidekick for the main character? Or is she a main character herself? Again, these scenarios are of increasing difficulty.
Writing from the point of view of a "foreign" character is particularly hard. Depicting her inner thoughts in a realistic way will be much more difficult than having her interact plausibly with a character from your own culture.
Nationality is not a personality type
If you wish to avoid stereotype, you should put as much work into developing the foreigner's distinct personality as you would for any other character. As you do so, you will have to keep the foreign character's background and experiences in mind at all times.
Suppose your character is an extremely devout Christian. In the USA, this makes him or her part of mainstream society; in the UK or France, a bit of an oddball; in Iran or China, part of a persecuted minority; in Syria, in fear for his life. His attitude towards his religion and other people will be shaped accordingly.
More generally (and without getting too deeply into psychology), any character's thoughts and actions will be determined by the interaction of experience with inherent personal traits.
You won't get everything right
You will find it very difficult to write from the POV of a character from another culture, unless you yourself have lived there for a very long time. I am a Canadian who has lived in the UK for the last 24 years, but I still occasionally run up against aspects of British culture I didn't know about. There is no magic solution; you just need to do your research, and if at all possible get help from a native of the country.
It's worth making an effort
If you don't do enough research, your character will be at best annoying, and at worst grossly offensive, to anyone familiar with the culture in question. This can kill the reader's interest in your story.
A good example appears in "The System of the World," an epic historical novel by Neal Stephenson. It includes a Scottish character made up entirely of national stereotypes. Everything this character says and does makes it clear he was made up by an American writer, who probably was trying to be funny and apparently has never met anyone from Scotland. I ended up putting the book down to find something more enjoyable to read.