Take out your cryptographic sequencer and hold L1 and R2. Rotate the right analog clockwise. Do this until Batmans head becomes big. All enemies will have a big head as well.
Using the cryptographic Sequencer, set the coordinates to 200, 500. A voice will speak the following numbers: 3-20-26-18-26-16-24-1-11-4-24-9-3-8-5-2-12-18-6-16-7-11-3-10-17-5-13-4-21-8. To decode requires a bit of work. First set each number to a letter in the alphabet but in reverse so that Z=1, Y=2, X=3 and so on. From there you use a special cipher known as a Vigenere Cipher that requires a keyword to translate. By using the keyword "scarecrow", the message is translated to "FEAR WILL TEAR GOTHAM CITY TO SHREDS". Due to the keyword being scarecrow, it could be implied that Scarecrow is behind at least this message and possibly more.
Go to the Riddlers Challenges and go to Custom Challenge. Select the first map and under modifiers choose Takedown Projectiles. This will make it so that your batarang will knockout enemies in 1 hit. Spam the batarang through all 4 rounds knocking out the enemies without getting hit once and you will get the trophy.