I'm not so sure what you exactly meanwith "taboo drama" but I guess a drama with taboo themes..?
SO I'm gonna start off with Goodbye to Goodbye. I t's about a young couple that discovers that the girl is pregnant( they're not married yet), and the drama is basically about how the girl deals with her situation. It's really good and it definitely portrays a taboo (at least in Korea, it's still a taboo)
Next one is Ho Goo's Love.. again pregnancy without marriage. It's one of the sweetest dramas I've seen.
Eulachacha Waikiki okay so because it is a comedy drama of course they showed it in a "funny" way but women having facial hair is almost everywhere still a taboo and they nailed some scenes regarding that so much.. so.. yeah, but the drama is really worth watching
I don't know wether they fit or not but It's Okay, That's Love & Kill Me Heal Me are both about Menatl Illness, eventhough both are very romantiziced so don't expect too much for that matter...
And the last and probably most shocking one is *drum rolls* The Judgement. This drama is a bit like 13 Reasons Why but like ten times more shocking. It was so good but horrifiying and You really need to have strong nerves to watch it, but I think this drama suits the Taboo Drama most.