Here is the full list of all 14 Anomaly Warzone Earth trophies - there are 7 bronze and 7 silver.
Destroy 5000 towers
Complete both co-op modes
Complete Tokyo Raid
Complete Baghdad Mayhem Rearmed
Complete Single Player Campaign
Use 4 different abilities simultaneously
Complete Baghdad Mayhem
Earn 10 gold medals within the campaign
Fully upgrade a unit (3 stars)
Boost 20 abilities while playing co-op mode
Use one Smoke Screen ability to protect 6 units
Collect 15 Carusaurum Caches
Collect 20 abilities
Destroy 10 Towers