This is when Xehanort possesses Terra's body and Terra has to fight to get it back. Not only was it a scary and unexpected boss fight. It was frustrating because you had to defeat Xehanort as yourself, then when he possesses Terra's body, you have to fight that battle again, and never die, not once.
A runner's up is definitely the boss battle between Ventus and Vanitas. He was a difficult boss to pin down, and when he melds into darkness, it's nearly impossible to keep track of him. Once again you have to fight Vanitas twice, and not die the second time to reach a final boss fight using only link commands without dying.
Kingdom Hearts Birth by Sleep had some of the most difficult boss battles.