Here is the full list of all 34 GUNDAM VERSUS trophies - there are 18 bronze, 11 silver, 4 gold and 1 platinum.
Unlock 1 navigator
Fought 100 online versus battles
Reached Mobile Suit Level 10 (not including ADD-ON Mobile Suits)
Defeated 25 waves in Ultimate Battle
Cleared 5 Trial Battle routes
Reached Player Level 50
Fought 10 online versus battles
Defeated 10 waves in Ultimate Battle
Reached Player Level 10
Cleared 1 Trial Battle route
Reached Mobile Suit Level 5 (not including ADD-ON Mobile Suits)
All Trophies Acquired
Cleared 10 Trial Battle routes
Achieved SSS rank in 5 Trial Battle routes
Achieved SSS rank in 10 Trial Battle routes
Cleared Easy Survival in Ultimate Battle
Cleared Normal Survival in Ultimate Battle
Defeated 50 waves in Ultimate Battle
Reached Player Level 100
Reached Player Level 300
Reached Mobile Suit Level 20 (not including ADD-ON Mobile Suits)
Acquired 10 Strikers (not including ADD-ON Mobile Suits)
Acquired 30 Strikers (not including ADD-ON Mobile Suits)
Acquired 50 Strikers (not including ADD-ON Mobile Suits)
Acquired 10 Emblems (not including ADD-ON Mobile Suits)
Acquired 20 Emblems (not including ADD-ON Mobile Suits)
Acquired 30 Emblems (not including ADD-ON Mobile Suits)
Acquired 10 Titles (not including ADD-ON Mobile Suits)
Acquired 30 Titles (not including ADD-ON Mobile Suits)
Acquired 50 Titles (not including ADD-ON Mobile Suits)
Fought 500 online versus battles
Fought 1000 online versus battles
Unlock 3 navigators
Unlock 5 navigators