The below section of the guide to Marvel's Spider-Man you will find a breakdown of the "Cat's Craddle" side quest.
Mission's starting location: Upper West Side
Reward: 250 XP
In order to unlock this side quest, you have to find all the mascots hidden by Black Cat. Thanks to that, you shall unlock the hideout of the elusive girl. Go to the old train depot - on the right, you will find a hidden entrance.
There will be a ton of Black Cat's loot waiting. You can browse the stash - Peter will find a voice recorder with a message from the girl. As it turns out, it was all a set-up, and Spider-Man has unwittingly helped the Cat with another heist.
The mission will end with partial success - although you didn't manage to catch Black Cat, Peter will get a new costume. The developers also announced that the story of the Cat will be further explored in a DLC.