Here is the full list of all 37 Girls und Panzer: Dream Tank Match trophies - there are 22 bronze, 9 silver, 5 gold and 1 platinum.
Acquire all Tanks.
Clear all schools in Domination Battle.
Clear all Extra Missions on Extreme Difficulty.
Clear all Extra Missions on Hard Difficulty.
Clear all Extra Missions on Normal Difficulty.
Clear Story Battle.
Clear Story Battle with all characters.
Deal a lot of damage, achieve a high reload rate, and end the match with your attack (excluding Free Match, Custom Match, and Friend Match). (Includes giant BOCO.)
Perform Napoli-turn.
Destroy more than 50 enemies cumulatively while Drifting (excluding Free Match, Custom Match, and Friend Match). (Includes giant BOCO.)
Destroy more than 30 Heavy Tanks cumulatively (excluding Free Match, Custom Match, and Friend Match). (Includes giant BOCO.)
Direct an ally through the Command & Control Panel.
Participate in a Free Match.
Activate Panzer High.
Use a Support Card.
Clear all Exhibition Matches.
Perform Sloped Armor Guard.
Destroy enemy tank treads.
Turn the tides with a decisive shot (excluding Free Match, Custom Match, and Friend Match). (Includes giant BOCO.)
Attack the enemy's weak spot.(Includes giant BOCO.)
Destroy a hidden BOCO.
Achieve a high hit rate (excluding Free Match, Custom Match, and Friend Match).
Destroy an enemy using scope mode.(Includes giant BOCO.)
Perform a Drift.
Activate a Tank Commander Skill.
Perform Boost dash.
Customize a tank.
Clear all Beginner's Training.
Destroy an enemy.(Includes giant BOCO.)
Perform Quick reload.
Obtain all trophies.
Acquire all Tank Colors.
Acquire all Decals.
Acquire all Crew and Support Cards.
Exceed 20 hours of Match time.
Player Level above 80.
1-hit-K.O. more than 50 enemy tanks cumulatively (excluding Free Match, Custom Match, and Friend Match).