Here is the full list of all 51 Disgaea 4 Complete+ trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Start a new game by selecting...New Game.
Complete all other trophies.
Inflict 10,000,000,000 damage.
Defeat Tyrant Overlord Baal in the Land of Carnage. "Whosoever unlocks this trophy, shall possess the title of Tyrant Overlord."
Collect all types of items.
Collect all Pirate Ship parts.
Have characters of every rank of every creatable class.
Watch every special skill animation.
Clear all X-Dimension stages. "You've conquered Dimension X!"
Defeat Pringer X in the Land of Carnage. "Pringer X is back, baby!"
Clear Ep. 1: Rebels of Hades.
Clear Ep. 2: Prinny Wars.
Clear Ep. 3: Enter the Final Weapon.
Clear Ep. 4: Death Emizel's Death.
Clear Ep. 5: The Angel of Avarice.
Clear Ep. 6: The A-Virus Pandemic.
Clear Ep. 7: Tyrant vs. President.
Clear Ep. 8: Final Boss vs. Final Boss.
Clear Ep. 9: The Moon, Earth, and the Promise!
Clear the main story, and begin the Post-Game.
Go to the Land of Carnage and regret it.
Watch Fenrich's epilogue. "All is for my Lord."
Watch Fuka's epilogue. "Come, iron roc!"
Watch Desco's epilogue. "Cretins...bow down and worship me! For I am Desco!"
Watch Emizel's epilogue. "Wandering messenger of twilight, show me the ways of this world!"
Watch Artina's epilogue. "Mother of the sublime glow, bring purity to the swirling evil!"
Defeat God (self-proclaimed). "Infernal demon, follow my order and present your vile soul!"
Clear the Flashback Episode. "Demon trapped in fire, I shall temporarily free your chaotic soul. Now! Become my power!"
Clear the Fuka & Desco Show. "Final Formation! We are Tri-Angels!"
Win the Netherbattle Tournament. "I want my own catchphrase."
Clear the Time Leap story. "Brave warrior, hear my voice... Become the skyward sword that pierces the darkness, and crush my enemies!"
Defeat Axel in the Post-Game and make him an ally. "Axel, on staaage!"
Defeat Archangel Flonne in the Post-Game and make her an ally. "Chaos sucks! Guardian of justice, Justice Flonne!"
Defeat Raspberyl in the Post-Game and make her an ally. "Which Honor Student wants to take my lesson?"
Defeat Etna in the Post-Game and make her an ally. "Look at my body and drool!"
Defeat Laharl in the Post-Game and make him an ally. "Taste the power of Overlord Laharl!"
Defeat Asagi in the Post-Game and make her an ally. "I'll show you my Super Miracle Heroine Powers!"
Defeat Prinny Kurtis in the Post-Game and make him an ally. "Can you handle Mach 5!?"
Defeat Zetta in the Post-Game and make him an ally. "I'll show you what a real strategy RPG is all about!"
Capture an enemy.
Lose a battle.
Persuade by force 3 times.
Explode ten Prinnies in a row.
Open all treasure chests in the base.
Clear 30 floors in the Item World.
Max out the Rosen Queen Co. customer level.
Inflict 100,000 damage.
Destroy the Axel statue in battle.
Max out an item's level.
Train 100 times.
Get over 100,000,000 HL.