Here is the full list of all 13 War Thunder trophies - there are 9 bronze, 3 silver and 1 gold.
Destroy 3,000 player vehicles in Random Battles
In Random Battles, get these five battle achievements: Mission Maker, Hero of the Sky, Thunderer, Heavy Metal Hero and Wing Breaker.
In Random Battles, destroy 100 player units while in a tank
In Random Battles, win 10 battles at rank four for the USA (battle activity: 50%)
In Random Battles, destroy a player airplane with a rocket. Complete the Mission.
In Random Battles, win a battle at rank five with first place in the match statistics (battle activity: 50%)
In Random Battles, destroy 500 vehicles while in an airplane using bombs
In Random Battles, destroy 100 player units while in an airplane
In Random Battles, destroy 50 airplanes with an anti-air gun
In Random Battles, win 10 battles at rank four for the USSR (battle activity: 50%)
In Random Battles, win 10 battles at rank four for Britain (battle activity: 50%)
In Random Battles, win 10 battles at rank four for Germany (battle activity: 50%)
In Random Battles, win 10 battles at rank four for Japan (battle activity: 50%)