Well, first off, the game is set in a much earlier point in Batman's life. And it seems that up until this Christmas Eve, he had dealt mostly with mobster types like the Falcones, Black Mask, Penguin and so on. He wasn't even familiar with Killer Croc even though he appeared in the beginning of the game. Not to mention that this is the first appearance of big villains like the Joker or Riddler into this universe, and others like Two-Face and Scarecrow apparently don't exist yet.
As to how crazy it is to run into all of those villains in the same night, remember that Bane, Deathstroke, Copperhead, Shiva, Deadshot, Electrocutioner and Firefly are paid to go after Batman - they are hired assassins that have come to Gotham with the specific purpose to meet Batman and take him out. And others, like Mad Hatter or the Riddler seem to be emerging just now because they want to take advantage of the overall chaos in the city caused by Batman's war against Black Mask and the assassins with the police in the middle; but the complexity of their plans and preparations suggest that they each have been planning it for some time now. It's just that this particular Christmas Eve is a perfect opportunity.