In CT:DS, the Lucca shade gave me a lot of trouble but that was mostly because my current party wasn't particularly suited for that battle. The Nu boss in the Lost Sanctum: Past took quite a while for me to overcome too, and the Dream Devourer actually killed my party the first time I fought it.
In Chrono Cross, Miguel and Dario stand out as the really difficult fights in my memory. Like many others, I had both Lynx AND Harle in my party when I fought Miguel, and that was just painful. If I remember correctly, I even tried to run away but instead of letting me recover and switch out my equipped characters Miguel said something about resisting Fate and re-engaged me! And Dario...OUCH.