In order to earn the trophy that's called "Catch!", you'll need to catch your own Batarang.
First off, you're going to need the Remote Control Batarang. Earn enough experience points to get a level and unlock the RCB as an upgrade.
Once that's done, if you are in an area free of enemies, make sure you're an open space.
Next, have the RCB equipped and throw it. Make sure it is far away from you before maneuvering it around and making it swing towards your direction. If you have it pointed back to Batman, chances are that Batman will catch it. If he does so successfully, the trophy will unlock.
I've provided a video solution from InfraRedPS. All credit goes to him for playing to get this trophy, then uploading the video to show how it's done.
Have fun and good luck!