for this you need spiderman
The location of black cat is north west of the circus. On the map she has white hair she is very easy to spot. When you find the location you need to shoot you web at the hooks to activate the door and open it. once you get in side use your spidey scences. when you use it a leaver will appear. pull it and it will open a box in the room with black cats character token inside.
When you spend 150,000 studs on the token the achievment should pop
[Edit] red compass pointers point NORTH.
that NORTHWEST should be SOUTHEAST - Just beside the Taking Liberties Icon.