that you do not need to face?)

[Spoiler alert!!!]

For example, in the SEGA Dragon Crystal game there are enemies that only attack you if you accidentally hit them! In this case their will follow you and try to kill your character.

What are the games that does have characters or enemies that are so powerful than your character or even more powerful than the main character? Some game series does feature powerful characters that could be a challenge, sure into most of those aforementioned games the player have a party of characters to face the single 'opponent'!

I think that this is common into some games series like:
Lufia
Final Fantasy
Dungeons & Dragons