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