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