I don't know about all of you, but I thought these were some pretty hard boss battles:
I had trouble with Alduin atop the throat of the world. I was about level 19 but I came back around level 33 with lots of health potions and stamina potions. I Later went on to get most of the dragon priests, which were easy for me. The enemies I actually have problems with are Briarhearts. When i was getting the piece of mehrune's razor from (Hag's end I Believe.) the Briarheart located there had Two Ebony war axe's, and I was around level 22. Luckily, I had the Shadowcloak Ability and got the jump on Him. Before, he simply power-attacked me and I Died. The Most Hardest Enemy I have Ever faced in skyrim before, EVER, had to be the first Elder dragon fought, before I got spellbreaker. (Which when the ward Is Completely charged can Actually Nullify An Ancient Dragon's fire.) When was I leaving the Falkreath Sanctuary and I was heading North to kill Hern, I heard a Roar. Shortly after, It pummeled me to the ground with ease.
What Is the hardest boss or enemy you've ever faced?