There are 9 new Trophies in this DLC.

Bronze

The Used to be Adventurers    
Ensure all three Colossal Archers reach the front lines at the Paradise Court battle in the Themyscira: The Gates of Tartarus raid    

Olympian    
Complete the Themyscira: The Gates of Tartarus raid in 20 minutes or less

In Prime Time    
Finish the Prime Battleground Raid in 15 minutes or less

Timely Closing Agruments    
Defeat the Prosector and Defense Attorney within 10 seconds of each other in the South Gotham Courthouse Alert    

Jury Tampering    
Stack the jury with 12 humans, not allowing any Brainiac Jurors to be transported to the Bailiff in the South Gothm Courthouse Alert

Silver

Prime Numbers    
Defeat all three Prime Avatars without destroying any of the Brainiac Spawners

Bottle Opener    
Complete 250 Battle for Earth Duos    

Guilty On All Charges    
Allow all Sentences to run their full course when fighting the Supreme Justice in the South Gotham Courthouse Alert

Uncover the Truth    
Complete all of the Collections, Briefings, and Investigations available in the Battle for Earth DLC

http://www.ps3trophies.org/game/dc-universe-online/trophies/