Here is the full list of all 41 New Gundam Breaker trophies - there are 22 bronze, 15 silver, 3 gold and 1 platinum.
Earn all trophies
Finish 30 complete MS part sets
Acquire 50 Melee Weapon parts
Clear all bonus missions
Clear all of Recoco’s missions
Clear all of Shion’s missions
Learn 5 Searcher Frame abilities
Finish 10 complete MS part sets
Clear all of Chinatsu’s missions
Clear 30 missions with Rank S
Acquire 50 Ranged Weapon parts
Learn 5 Enchanter Frame abilities
Clear all of Ryoko’s missions
Clear all of Iori’s missions
Learn 5 Gunner Frame abilities
Acquire 30 Shield parts
Acquire 500 parts
Clear all of Marika’s missions
Learn 5 Striker Frame abilities
Finish a complete MS part set
Clear all of Yui’s missions
Clear 10 missions with Rank S
Acquire 20 Head parts
Acquire 20 Backpack parts
Play a Quick Match
Acquire 20 Leg parts
Acquire 20 Body parts
Acquire 20 Arm parts
Learn 5 Balance Frame abilities
Get 1st Place in a Multiplayer match
Form a team/room and play a Multiplayer match
Win a Network Battle
Join a team/room and play a Multiplayer match
Clear a quest to destroy a Warship
Clear a quest to destroy a Mobile Armor
Acquire 5 Builders parts
Use an EX Skill from a part you exchanged during a mission
Exchange parts during a mission (except during tutorial)
Clear a mission with Rank S
Clear a quest to destroy a Perfect Grade
Use the Cube to Recover a part you stole during a mission