Successfully complete one of the following tasks to get a trophy:

Commando (Silver): Complete the game in campaign mode without seeing the game-over screen and without leaving the action. (1 or 2 players)
Dodge Master (Bronze): Win a battle in Battle or Online Battle mode without getting hit.
First Blood (Bronze): Destroy 1 enemy tank.
Ludicrous Speed (Silver): Complete the game in campaign mode in 60 minutes or less without leaving the action. (1 or 2 players)
Master Exploder (Bronze): Destroy 150 enemy tanks with a rocket launcher in any game mode.
One-Tank Army (Bronze): Clear the game campaign mode in solo.
Online Recruit (Bronze): Play 1 online game.
Online Veteran (Bronze): Play 99 online games.
Pyromaniac (Bronze): Destroy 150 enemy tanks with a flamethrower in any game mode.
Rampage (Bronze): Destroy 25 enemy tanks without getting hit in any game mode in one game session.
Tank of Doom (Gold): Destroy 10,000 enemy tanks.
The Pacificator (Bronze): Survive 120 seconds in a battle without shooting in Battle or Online Battle mode.
Winning Streak (Bronze): Win 10 battles in a row in Battle or Online Battle mode.