Looking for dramas where the psychological part is very heavy, a drama that shows mystery and you don't whats real or not, something psychological like Joint Security Area, or these american movies, Memento, The Machinist, Fight Club, Shutter Island, or Jacob's Ladder, something like those, when a character, he or she is crazy and doesn't even know it

If you're into romance, try It's  Okay, It's Love. This particular drama is an art! ^^ Another one is Kill Me, Heal Me. 

 Bleng:

If you're into romance, try It's  Okay, It's Love. This particular drama is an art! ^^ Another one is Kill Me, Heal Me. 

I've seen those, looking for something darker

You can try Love Me If You Dare. I'm still not sure if the main character were actually crazy or not ;)

i would suggest; very highly: TEN, TEN 2

highly: God's Quiz, Piece(JP), God's Gift 14 Days

give it a shot: Gap Dong, Save Me, Hello Monster(this is one is not as dark)

they are not exactly what you are asking for but are pretty close.

Hello Monster/I Remember You- kdrama starring Seo In Guk, Park Bo Gum and Jang Na Ra. It’s a crime show, but it focuses on what makes a murderer (or ‘monster’) and if you can save them and whether they’re worth saving.

Kazoku Game- jdrama starring Sakurai Sho. It’s about a seemingly perfect family who hire a tutor with questionable methods for their younger, ‘problem’ son. He begins to reveal the family’s secrets and true nature but on the way they discover that he has secrets of his own. This drama is phenomenal and the type which constantly keeps you guessing- you’re never sure who you can trust and just when you think you’ve figured out the truth, it changes. All of the family members are interesting psychological studies, but the elder son and the tutor are some of the most fascinating characters in drama history!

 RomanticArisu:

Hello Monster/I Remember You- kdrama starring Seo In Guk, Park Bo Gum and Jang Na Ra. It’s a crime show, but it focuses on what makes a murderer (or ‘monster’) and if you can save them and whether they’re worth saving.

Kazoku Game- jdrama starring Sakurai Sho. It’s about a seemingly perfect family who hire a tutor with questionable methods for their younger, ‘problem’ son. He begins to reveal the family’s secrets and true nature but on the way they discover that he has secrets of his own. This drama is phenomenal and the type which constantly keeps you guessing- you’re never sure who you can trust and just when you think you’ve figured out the truth, it changes. All of the family members are interesting psychological studies, but the elder son and the tutor are some of the most fascinating characters in drama history!

Seen Kazoku Game, It's ranked 5 in all of the Asian dramas i've seen, 82 total i've seen, and imo, I think it's the best Japanese drama ever, of course there are good ones but so far, no other Japanese drama has top Kazoku Game 

Defendant - main character wakes up in jail with no memory, charged with killing his wife and daughter. Did he really do it??

Circle - follows story in present and future. they seem like two separate stories at first but youll see how they merge later on. in both time lines main character is looking for someone...theres more to this but how to say without spoilers....

Death Note Drama - theres a drama, movie, anime, manga... to be honest i think all the versions are great but Light in the drama version is the best! Whoever's name is written in a death note will die. main character uses it for "justice"

Ahh I wanted to recommend Kazoku Game too but you've seen it XD

It's Okay that's Love

I second @RomanticArisu's recommendations!

Also, though all of them are jdrams: 

Aishite tatte, Himitsu wa Aru (you have to wait until the last episodes for the plot twist)

Boku no Yabai Tsuma (this one has so many twists along the plot)

Byakuyako (this one is one of the darkest ones I've seen) 

Liar Game!

I loved it. (I watched the Korean version, but the original is Japanese.)

-- That's what I wanted to write, but I see that you have already watched it.  :-)

My recommendations are

Secret Investigation Record

 Shadows in the Palace 

Try Bloody Monday. I bet you'll love it!