Gigantic Monster/Beast

So, my sister and I (who I have played Minecraft with for years) were talking about how cool it would be to have a rare, almost unpredictably-occuring mob that was basically a large, quadruped beast that had certain abilities like: (a) ramming through certain weaker blocks such as wood and dirt, (b) pouncing on prey, such as cattle, livestock, and yes, the player, and (3) getting tired after much resistance from the player- causing it to run away- but coming back later on depending on if he can track you or not.

I don't know. Just seems like it would be a really cool thing to have a blight such as that that might or might not come up, causing your friends and you to band together and defeat the beast. Just seems like a really cool concept to me, and might provide more of a challenge for the players that don't really want to spend the time it takes to find an End portal or Nether portal- give them an Overworld boss, in a sense.

It could be a reoccuring thing every once in a while as well, so you would need to build fortifications to your base. Maybe it could be a "Hard Mode only" type deal?