Here is the full list of all 40 Neptunia Virtual Stars trophies - there are 28 bronze, 6 silver, 5 gold and 1 platinum.
You defeated the powerful enemy in Cookunia.
You used the Finish Drive for the first time.
You activated the Finish Execution for the first time.
Cleared Chapter 3.
You defeated the powerful enemy in NeoTube.
You revived one facility in the NeoTube Plaza.
Cleared Chapter 2.
You did Guest Connect for the first time.
You filled in 15 entries in the Anti Encyclopedia.
You used the Emotional Overdrive for the first time.
You acquired a V-Cube for the first time.
Cleared Chapter 1.
You activated Tokimeki Flash for the first time.
Cleared the Prologue.
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Cleared Chapter 4.
Cleared Chapter 5.
Cleared Chapter 6.
Cleared Chapter 7.
Cleared Chapter 8.
Cleared Final Chapter.
You defeated the powerful enemy in Novelia.
You defeated the powerful enemy in Twinia.
You defeated the powerful enemy in Gaminion.
You defeated the powerful enemy on Planet Obsoletia.
A character's level became 30.
A character's level became 50.
A character's level became 100.
You filled in 50 entries in the Anti Encyclopedia.
You filled in 80 entries in the Anti Encyclopedia.
You used the Video Battler for the first time.
You used the Video Battler 100 times.
You tried BeatTik for the first time.
You received over 20 presents at once during BeatTik.
You acquired a total of 100,000 Rank Points.
You acquired a total of 500,000 Rank Points.
You gained the highest broadcast rank in BeatTik.
You acquired 30 types of V-Cubes.
You maxed the ranks of all facilities in the NeoTube Plaza.
You activated the Finish Drive's extra attack for the first time.