Problematic meaning - *****y ,delinquent, cold,people are scared of her - any of these Guy cool or bad ass - clever , not a player( a must ), no interest in girls, quiet, literally kicks ass or kicks ass with his wits The ones I have watched that have these school 2013- the romance is a bit lacking but I did enjoy the small part of it with go nam soon and the girl who only cared about grades Innocent man ,Salaryman , please take care of the young lady, couple or trouble, the snow queen- all btchy girls and the guys were all very likeable zenkai girl- girl only cares about being successful Monstar- Oh my fck Kim Nana is my all time fav right now for female leads her and sun woo need to get together!! -would definitly like it if there is someone that is close to kim nana.
Do you want both girl and guy to fulfill your conditions or one is enough?
devil beside you, Goong, que sera sera, a love to kill, mischievous kiss(there are 4 versions i believe), ps man; are all bad guy good girl type of dramas. boys over flower(3 versions); its also about a bad guy but the girl is pretty though.
Sry if you've seen already (too tired now to re-read post), but you can see if any of these'll do: :) Wild Romance Witch Yoo Hee The Vineyard Man My Sassy Girl (Movie) Miss No Good (so-so) Me too Flower Kimi wa Petto Bull Fighting
Me Too, Flower? That's the only one I can think of now :D
Try the movie Love 911 (Bandage), the main girl is very very tough and the guy is just like your description :D http://mydramalist.com/korean-movie/4642/love-911