Here is the full list of all 51 Aquapazza: Aquaplus Dream Match trophies - there are 39 bronze, 9 silver, 2 gold and 1 platinum.
[NETWORK RANKED MATCH] Defeat your opponent with a Splash Art.
[NETWORK RANKED MATCH] Defeat your opponent with a Partner Assist.
[NETWORK RANKED MATCH] Set both title slots and battle online.
[TRAINING] Train for 5 minutes straight.
[NETWORK PLAYER MATCH] Fight for the first time.
[NETWORK RANKED MATCH] Win 3 games in a row.
[NETWORK RANKED MATCH] Defeat your opponent with a Super Move.
[NETWORK RANKED MATCH] Earn your first victory.
[NETWORK RANKED MATCH] Fight your first battle.
Complete [STORY] or [ANOTHER STORY] with the Normal control scheme.
[STORY] Defeat the final boss.
[STORY] Complete Stage 7.
[STORY] Complete Stage 5.
[STORY] Complete Stage 3.
[STORY] View the opening movie.
You earned all other trophies in AquaPazza!
[STORY] Defeat all final bosses.
[ANOTHER STORY] View the opening movie.
[ANOTHER STORY] Complete Stage 3.
[ANOTHER STORY] Complete Stage 5.
[ANOTHER STORY] Complete Stage 7.
[ANOTHER STORY] Defeat the final boss.
[SCORE ATTACK] Meet the last boss.
[NETWORK RANKED MATCH] Obtain a Grade of C with any character.
[NETWORK RANKED MATCH] Gain all Character Titles for any character.
Hakuowlo: Defeat your opponent using Uitsualnemetia.
Hakuowlo: Withstood over 4,000 damage using Ointment of Tonburuchi.
Karulau: Land a combo that uses Gouga in the middle.
Karulau: Got a critical hit with Gouhajin in a combo.
Touka: Successfully perform well-timed inputs during all of Kikyo and follow up with Raikou Muei Zan.
Touka: Failed Shinmyosen at least 2 times during a single round.
Arawn: Lower your Emotion within 4 seconds of the round's start.
Arawn: Emptied your opponent's power meter using Rubedo and/or Magic Hunt.
Morgan: Shoot all of your arrows.
Morgan: Successfully hit with Bone Breaker at least 2 times in a single round.
Riannon: Hold Stella Maris for more than 10 seconds.
Riannon: Performed any of the following moves: Fighting Sorceress, Element Cycle, or Revitalize.
Konomi: Cancel Satchel Upper! into Genghis Khan - 1192♪.
Konomi: Defeated your opponent with Mom's Killer Curry! during High Emotion.
Tamaki: Get 10 extra hits with Iron Claw (C).
Tamaki: Performed a combo of 25 or more hits without using a Partner Assist.
Manaka: Perform 5 moves from the front step/back step follow-ups after certain moves.
Manaka: Used This is My Hideaway to teleport to the other side of the screen.
Multi: Defeat your opponent with Serio's attack in Sisters' Housecleaning.
Multi: Slipped on your own Cleaning is My Purpose.
Sasara: Block at least 3 attacks using the guard points of special moves during a single round.
Sasara: Deflected your opponent's attack using Parry.
Oboro: Call Dorry or Guraa at least 3 times during a single round.
Oboro: Defeated your opponent with Kagenui Bakumetsudan.
Chizuru: Defeat your opponent with Forgive Me…
Chizuru: Made your opponent enter Low Emotion 3 times in a single round.