Welcome to Player Attack!
If you feel that Warner Bros is playing with your emotions, rest assured it's (probably) not intentional. First, there was the joyful announcement that Catwoman would be a playable character in Batman: Arkham City. Then the revelation that you'd need an online pass to unlock her character.
Finally, once the game was launched, copies were apparently shipped without the all-important Catwoman code, or containing a code that simply didn't work.
The publisher has claimed the issue affects less than 0.5% of total shipped copies of Batman: Arkham City, but it doesn't take much to make a few people very unhappy.
In a public statement, WBIE explains:
While the number of affected versions is very small, WB Games apologises for any inconvenience this has caused and we are committed to getting these issues resolved as quickly as possible.
If you are affected, please call customer support (that's 410-568-3680 in the United States), email email@example.com, or visit the official website: community.batmanarkhamcity.com/support.
...even if you do have a code, and it does let you download the content, you may not be out of the woods - reports have started popping up that the DLC may be corrupt upon install, but WBIE has refrained from acknowledging that problem at this stage. If, again, it's affecting such a tiny minority, it's more than likely a fault at the user's end, rather than anything the publisher can control.