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
Unlock all playable Mobile Suits
Obtain all licenses
Clear all "Mobile Suit Turn A Gundam" history missions
Clear all "Mobile Suit Gundam Wing" history missions
Clear all "After War Gundam X" history missions
Clear all "Mobile Fighter G Gundam" history missions
Clear all "Mobile Suit Victory Gundam" history missions
Clear all "Mobile Suit Gundam F91" history missions
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
Complete the sound gallery
Unlock all playable characters
Shoot down 100,000 enemies
Clear all "Mobile Suit Gundam 0083" history missions
Complete the character gallery
Clear all "Mobile Suit Zeta Gundam" history missions
Exceed 200 plays
Clear all "Mobile Suit Gundam" history missions
Raise any one character's pilot level to 50
Clear all story missions
Reach tech level 10 in the Mobile Suit lab
Play online 100 times
Complete the Mobile Suit gallery
Shoot down 1,000 enemies online
Exceed 100 plays
Completely finish either of the story missions "Those Who Understand" or "Those Who Fight."
Play online 20 times
Shoot down 10,000 enemies
Shoot down 100 enemies online
Obtain more than 10,000 G