Here is the full list of all 53 BlazBlue: Central Fiction trophies - there are 42 bronze, 8 silver, 2 gold and 1 platinum.
[Story] Completed the entire main story.
[Story] Completed episode 10.
[Story] Completed episode 7.
[Story] Completed episode 4.
Successfully executed 10 Astral Finishes.
Successfully used Rapid Cancel 10 times.
[Story] Completed episode 1.
[Gallery] Opened up all guest illustrations.
Successfully executed 10 throw-escapes.
[Gallery] Played back the credits.
Successfully executed a Guard Crush 10 times.
Successfully executed a 100-hit combo.
Successfully executed an instant block 10 times.
[Network] Customized your own room.
[Network] Used the quick message feature in an online lobby.
[Network] Used a face icon in an Online Lobby.
[Network] Added a player to your favorites.
[Item Shop] Played back a single location test voice.
[Arcade] Completed the arcade mode.
[Replay Theater] Played back another person's replay.
[VS] Won with difficulty set to Normal or higher.
[Training] Played back another person's key history.
[Tutorial] Played through a character's strategy guide.
[Training] Used the key record / playback feature.
[Tutorial] Completed Tutorial Mode.
Mastered BlazBlue Centralfiction.
[Challenge] Completed a total of 10% of the challenges.
[Challenge] Completed all of a single character's challenges.
[Story] Completed all sub stories.
[Glossary] Opened up everything.
[Abyss] Acquired 50 Grimoires.
[Abyss] Acquired 30% of all Skills.
[Abyss] Increased the level of a Grimoire to maximum.
[Abyss] Increased a character's level to 50.
[Abyss] Successfully extracted skills from the Grimoire.
[Abyss] Completed all normal stages 1 through 3.
[Abyss] Completed through stage 8.
[Score Attack] Completed all courses.
[Speedstar] Completed all courses.
[Item Shop] Purchased additional character colors.
[Network] Won a Ranked Match.
[Network] Reached LV 11.
[Network] Won "My room" match.
[Network] Won an online lobby match.
[Network] Changed your icon, plate, title, lobby character, and accessories.
[Network] Collected 50 pieces of furniture for your "My Room."
Dealt 10,000+ damage in a single combo.
Successfully executed 10 Distortion Finishes.
Successfully executed 10 Overdrive Finishes.
Successfully executed 10 Exceed Accels.
Successfully executed 10 Fatal Counters.
Successfully blocked 10 overhead attacks.
Successfully used Counter Assault 10 times.