In order to earn the trophy that's called "Streets of Gotham", you have to explore all three islands and search for militia checkpoints. If you are nearby one, the game will alert you to that checkpoint and it is up to you to destroy it in the way you see fit.
One piece of advice that I'll give is that you leave this as one of the missions for last as you should make sure to upgrade both Batman and the Batmobile to its fullest extent as best as possible. That way, you'll be fully ready to tackle on this trophy without much problem.
Here is an excellent video guide for this trophy, as it shows you all the locations and what's necessary to do for each checkpoint. All credit goes to BatmanArkhamVideos for creating and posting the guide on their Youtube channel.
Have fun and good luck!