Here is the full list of all 13 Tank Battles trophies - there are 10 bronze, 2 silver and 1 gold.
Complete the game in campaign mode without seeing the game-over screen and without leaving the action. (1 or 2 players)
Complete the game in campaign mode in 60 minutes or less without leaving the action. (1 or 2 players)
Destroy 10,000 enemy tanks.
Destroy 150 enemy tanks with a flamethrower in any game mode.
Destroy 150 enemy tanks with a rocket launcher in any game mode.
Clear the game campaign mode in solo.
Destroy 25 enemy tanks without getting hit in any game mode in one game session.
Survive 120 seconds in a battle without shooting in Battle or Online Battle mode.
Win 10 battles in a row in Battle or Online Battle mode.
Play 99 online games.
Win a battle in Battle or Online Battle mode without getting hit.
Play 1 online game.
Destroy 1 enemy tank.