Here is the full list of all 39 World of Warships: Legends trophies - there are 18 bronze, 17 silver, 3 gold and 1 platinum.
Simultaneously have 5 American or British commanders in your roster
Own 10 American or British ships in any proportion at the same time
Promote Commander to legendary rank 1
Simultaneously have 5 Japanese or German commanders in your roster
Promote a Commander to rank 11
Research a Tier V ship
Own 10 Japanese or German ships in any proportion at the same time
Promote a Commander to rank 7
Research a Tier III ship
Promote a Commander to rank 2
Install a ship upgrade
Survive and win any battle
Congratulations! You beat the game!
Play 100 Standard battles as a Destroyer
Play 100 Standard battles as a Cruiser
Play 100 Standard battles as a Battleship
Destroy 20 enemy ships in Standard battles
Destroy 200 enemy ships in Standard battles
Destroy 50 enemy ships with your torpedoes in Standard battles
Destroy more enemy ships than any other member of your team (at least 5) in a Standard battle
Win a Standard battle and survive while also obtaining the highest XP of your team
Win a Standard battle while being the sole survivor in your team
Win a Standard battle and survive while part of a Division
Win a Standard battle and survive while also earning 200,000 credits
Score 5 citadel hits in a single Standard battle
Set enemy ships on fire 7 times in a single Standard battle
Destroy enemy ship modules 100 times in Standard battles
Earn 20 ribbons (excluding the 'Target Hit' ribbons) in a single Standard battle
Capture a key area or base 3 times in Standard battles
Defend the base or a key area 3 times in Standard battles
Destroy at least 4 enemy ships in a single Standard battle with an American or British ship
Destroy at least 4 enemy ships in a single Standard battle with a Japanese or German ship
Destroy an enemy by fire that exceeds 50% of its HP in a Standard battle
Destroy an enemy ship dealing 50% or more damage with a single salvo in a Standard battle
Destroy an enemy by flooding that exceeds 50% of its HP in a Standard battle
Install 6 upgrades or modifications in any combination on a single ship
Unlock and install all modifications on a Tier VII American or British ship
Unlock and install all modifications on a Tier VII Japanese or German ship
Promote a Commander to rank 16