Here is the full list of all 51 Disgaea 4 Complete+ achievements.
Max out an item's level.
Defeat Prinny Kurtis in the Post-Game and make him an ally. "Can you handle Mach 5!?"
Go to the Land of Carnage and regret it.
Open all treasure chests in the base.
Destroy the Axel statue in battle.
Clear 30 floors in the Item World.
Defeat Zetta in the Post-Game and make him an ally. "I'll show you what a real strategy RPG is all about!"
Clear the Flashback Episode. "Demon trapped in fire, I shall temporarily free your chaotic soul. Now! Become my power!"
Lose a battle.
Defeat Asagi in the Post-Game and make her an ally. "I'll show you my Super Miracle Heroine Powers!"
Defeat Laharl in the Post-Game and make him an ally. "Taste the power of Overlord Laharl!"
Defeat Etna in the Post-Game and make her an ally. "Look at my body and drool!"
Get over 100,000,000 HL.
Inflict 100,000 damage.
Defeat Raspberyl in the Post-Game and make her an ally.
Defeat Archangel Flonne in the Post-Game and make her an ally. "Chaos sucks! Guardian of justice, Justice Flonne!"
Defeat Axel in the Post-Game and make him an ally. "Axel, on staaage!"
Max out the Rosen Queen Co. customer level.
Clear the main story, and begin the Post-Game.
Watch Artina's epilogue. "Mother of the sublime glow, bring purity to the swirling evil!"
Clear Ep. 9: The Moon, Earth, and the Promise!
Clear Ep. 8: Final Boss vs. Final Boss.
Clear Ep. 7: Tyrant vs. President.
Clear Ep. 6: The A-Virus Pandemic.
Clear Ep. 5: The Angel of Avarice.
Capture an enemy.
Clear Ep. 4: Death Emizel's Death.
Clear Ep. 3: Enter the Final Weapon.
Clear Ep. 2: Prinny Wars.
Clear Ep. 1: Rebels of Hades.
Start a new game by selecting...New Game.
Inflict 10,000,000,000 damage.
Defeat Tyrant Overlord Baal in the Land of Carnage. "Whosoever unlocks this achievement 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!"
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!"
Defeat God (self-proclaimed). "Infernal demon, follow my order and present your vile soul!"
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!"
Persuade by force 3 times.
Explode ten Prinnies in a row.
Train 100 times.
Complete all other achievements.