Here is the full list of all 59 Dengeki Bunko: Fighting Climax trophies - there are 50 bronze, 7 silver, 1 gold and 1 platinum.
Mikoto's Dream Duel cleared. "I hope we can dream together again!"
Miyuki's Arcade Story cleared. "I offer you my most sincere gratitude, on behalf of myself and my brother!"
You unlocked "Selvaria Bles" as a playable character.
Mikoto's Arcade Story cleared. "Thanks for being with me. You were a big help."
You've used Blast a total of 100 times. (Training mode doesn't count)
You've won after having 75% less health than your opponent. (Training mode doesn't count)
You've used Climax Arts a total of 100 times. (Training mode doesn't count)
You've used Impact Skills (including Impact Breaks) 500 times. (Training mode doesn't count)
Asuna's Arcade Story cleared. "Thanks for fighting alongside me."
You've called support characters 100 times. (Training mode doesn't count)
You've won using nothing but basic attacks. (Training mode doesn't count)
You won every round with a "Perfect". (Training mode doesn't count)
You unlocked "Akira Yuki" as a playable character.
Yukina's Arcade Story cleared. "Your help was sincerely appreciated!"
You called for support exactly when cooldown finished. (Training mode doesn't count)
You totally missed with a Climax Art. (Training mode doesn't count)
Both players called for support at the same time. (Training mode doesn't count)
Checked out "NOVELS".
You've won with the digits matching on the clock. (Training mode doesn't count)
Two Impact Skills (includes Impact Breaks) collided. (Training mode doesn't count)
Dengeki Bunko: Fighting Climax Play Has Begun. The ultimate battle begins!
You finished Dengeki Bunko: Fighting Climax. Thank you for playing!
Shana's Arcade Story cleared. "Thanks for fighting with me."
Kirino's Arcade Story cleared. "So um, you okay with... another life consultation sometime?"
Shizuo's Arcade Story cleared. "Playing the game with you felt good. Thanks."
Kuroyukihime's Arcade Story cleared. "I, Umm... Well... Thanks, just... thanks."
Tomoka's Arcade Story cleared. "Thank you very much, coach! Ehehehe!"
Kirito's Arcade Story cleared. "Thanks for fighting by my side. You were great!"
Taiga's Arcade Story cleared. "Um, Er... So... Thanks for helping, and stuff..."
Rentaro's Arcade Story cleared. "You were a huge help. I'll call you next time I got a job, partner."
Shana's Dream Duel cleared. "Let's dream together again sometime!"
Asuna's Dream Duel cleared. "I'm looking forward to our next dream together!"
Kirino's Dream Duel cleared. "We're gonna dream together again sometime, got it?!"
Shizuo's Dream Duel cleared. "It was fun sharing a dream with you! Later!"
Kuroyukihime's Dream Duel cleared. "Let's dream together again, okay...?"
Tomoka's Dream Duel cleared. "Let's play dream basketball again, okay? Ehehe."
Kirito's Dream Duel cleared. "Let's dream together again, okay!"
Taiga's Dream Duel cleared. "Your gonna help me in my dreams again... right?"
Miyuki's Dream Duel cleared. "We shall have to dream together again!"
Yukina's Dream Duel cleared. "Let's dream together again someday!"
Rentaro's Dream Duel cleared. "It was a tough fight, but fun. See you in dreamland again!"
You got 300,000,000 or more points in Score Attack.
You cleared Time Attack in 8 minutes or less.
You defeated 15 or more opponents in Survival Mode.
You participated in an online battle for the first time.
You've spent more than an hour in Training mode.
You've guarded against enemy attacks 1000 times. (Training mode doesn't count)
You've successfully escaped 50 throws. (Training mode doesn't count)
You've used Trump Cards a total of 300 times. (Training mode doesn't count)
You've used EX Special Moves a total of 500 times. (Training mode doesn't count)
You've successfully activated Reflection Guard 500 times. (Training mode doesn't count)
You've inflicted 10,000,000 damage on your enemies. (Training mode doesn't count)
You won by a Climax Art charged with two Trump Cards. (Training mode doesn't count)
You won within a 10 count. (Only when time speed is set to Normal; Training mode doesn't count)
You've lost with 2 Trump Cards and 5 Stock remaining on your Climax Gauge. (Training mode doesn't count)
You got all the special illustrations.
You got all the icons.
You got all the plates.
You got all the colors for a character.