Not so much the boss, but my own stupidity in not understanding a crucial game mechanic (though in my defense, it's never explained to you).
In Shining Force, you control a party of characters and participate in tactical turned based battles. These characters level up over time with a max level of 20. I reached a point in the game where all of my characters were level 20, so I figured it must almost be over. Then it wasn't.... and still wasn't. Gradually, my party became woefully underpowered. They'd do little dents of damage to enemies while getting 1-2 shot. I struggled through until I came across Chaos. He could OHKO anyone in my party and the damage I dealt to him was pitiful. If it was just him, I still don't think my party could have won, but he also has an army of minions, all of whom were stronger than anyone in my party. I tried many times, but ultimately decided that it was impossible.
Years later, I realized that there is a promotion system where after a character reaches level 10, you can promote them to a class that has much greater potential at the cost of a temporary stat decrease. Now it and its sequel are two of my favourite games.