There are a total of 10 Black Cat Journals (Audio Logs) in The Amazing Spider-Man 2. Finding all of these collectibles will earn you the Lover Trophy or Achievement.
All the other Audio Logs are not needed for any trophies or achievements and can be ignored.

Five of Black Cat's Journals can be found during Story missions. The other five are hidden in the open world. If you fully upgrade your Spider-Sense they will be highlighted on the mini-map when you get close to them.

In the Pause Menu under the "Messages" tab you can see exactly which logs have been found. Each one has its own number, so that you can keep track of what's missing.

TIMELINE:
#1 - Felicia Hardy's Journal Part 01 - 0:05
#2 - Felicia Hardy's Journal Part 02 - 0:49
#3 - Felicia Hardy's Journal Part 03 - 1:23
#4 - Felicia Hardy's Journal Part 06 - 1:52
#5 - Felicia Hardy's Journal Part 07 - 2:16
#6 - Felicia Hardy's Journal Part 09 - 2:35
#7 - Felicia Hardy's Journal Part 05 - 3:02
#8 - Felicia Hardy's Journal Part 04 - 3:33
#9 - Felicia Hardy's Journal Part 10 - 4:02
#10 - Felicia Hardy's Journal Part 08 - 4:31