How do you know if you beat batman arkham city?

I beat Batman: Arkham City but in the side mission (identity theft) batman says "i have to go to the batcave." I've been playing for a while waiting and stuff but it doesn't tell me to go to it. did batman just say that or do i really have to go there?How do you know if you beat batman arkham city?
you beat arkham city after completing this quest:

http://www.rarityguide.com/articles/arti鈥?/a>How do you know if you beat batman arkham city?
You do not need to go to to the Batcave. In the main game, there is no way to access it, anyway. He is talking about going back there to do research on Hush, the villian of the "Identity Theft" side quest, in order to stop him, after he is finished in Arkham City. You, as a player, don't go to the Batcave for this.How do you know if you beat batman arkham city?
I think its just an option. It isn't really necessary to do.
Batman just says that.

You don't go to the Batcave in Arkham City.