To earn this trophy that's called "Party Pooper", you will need to break up the party near the end of the game by defeating twenty thugs at the Visitor Center.
After you defeat Poison Ivy, make your way to the Visitor Center. Before entering, you will see four bad guys, including one that announces you as the guest of honor. Take out these thugs in any way you see fit. Make sure all of them are down before going inside.
When you do go in, you will see at least sixteen thugs "celebrating" this "occasion". Before you start the fight, I suggest you put three pieces of explosive gel in between them all, all three down the middle. They will not attack you unless you attack them first, so you'll be OK as you do this.
Once this is done, make your way to the entrance and then set them all off. All of them will be dizzied and this should give you a little time to execute ground takedowns on three-to-five thugs.
Most of them will get back up and it's time for you to fight. Make sure to constantly evade by jumping over them and then hitting them. If a thug happens to try and hit you, counter him by pressing
when lighting bolts appear above their head. Also, it's a good idea to use batarangs and even your ultra claw so that you can have an easier time dealing damage and giving yourself some breathing room.
Once you have knocked out all twenty thugs (again, four on the outside, sixteen on the inside), the trophy should be unlocked. I have provided a video of how this is done and this video comes from Batman Arkham Videos. Credit goes to that channel for creating and uploading the footage.
Have fun and good luck!