Here is the full list of all 38 Dynasty Warriors: Gundam 3 trophies - there are 24 bronze, 9 silver, 4 gold and 1 platinum.
Unlock all DYNASTY WARRIORS: GUNDAM 3 Trophies
Clear all missions
Friendship level of all characters reaches level 5
Complete the movie gallery
Clear all history missions
Clear all "Mobile Suit Gundam 00" history missions
Clear all "Mobile Suit Gundam Seed Destiny" history missions
Clear all "After War Gundam X" history missions
Clear all "Mobile Suit Gundam Wing" history missions
Clear all "Mobile Fighter G Gundam" history missions
Clear all "Mobile Suit Turn A Gundam" history missions
Unlock all playable characters
Obtain all licenses
Clear all "Mobile Suit Victory Gundam" history missions
Clear all "Mobile Suit Gundam F91" history missions
Complete the sound gallery
Clear all "Mobile Suit Gundam Unicorn" history missions
Clear all "Mobile Suit Gundam: Char's Counterattack" history missions
Clear all "Mobile Suit Gundam ZZ" history missions
Clear all "Mobile Suit Gundam 0083" history missions
Complete the character gallery
Clear all "Mobile Suit Zeta Gundam" history missions
Shoot down 100,000 enemies
Unlock all playable Mobile Suits
Clear all "Mobile Suit Gundam" history missions
Clear all story missions
Exceed 200 plays
Exceed 100 plays
Play online 100 times
Shoot down 1,000 enemies online
Raise any one character's pilot level to 50
Complete the Mobile Suit gallery
Completely finish either of the story missions "Those Who Understand" or "Those Who Fight."
Reach tech level 10 in the Mobile Suit lab
Play online 20 times
Shoot down 100 enemies online
Shoot down 10,000 enemies
Obtain more than 10,000 G