Here is the full list of all 51 Disgaea 5: Alliance of Vengeance trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Condition：Obtain all other trophies. Congratulations on getting all the trophies!
Condition：Clear Ep. 1: Prelude to Vengeance. The story of rebellion starts now!
Condition：Clear Ep. 2: Demon General. Madam Seraphina, hooray!
Condition：Clear Ep. 3: His Name is Zeroken. A silver white shadow that creates a storm...
Condition：Clear Ep. 4: Yellow, Rabbit, and Curry. I want curry, I want curry, I want curry, I want curry...
Condition：Clear Ep. 5: The One Who Controls Death. Kill and Recycle!
Condition：Clear Ep. 6: The Sixth Warrior. Dance of the Bristle Grass!
Condition：Clear Ep. 7: Past Struggles Part 1. Bro!
Condition：Clear Ep. 8: Past Struggles Part 2. Master!!!
Condition：Clear Ep. 9: The New Power. Guuurrryaaahhh!!!
Condition：Clear Ep. 10: The Memorable Special Sweet Curry. Our...beloved daughter...
Condition：Clear Ep. 11: Netherworld Extinction. They are all irreplaceable.
Condition：Clear Ep. 12: Unbridled Killia. The one who leaves destruction in his wake.
Condition：Clear Ep. 13: The Two Killias. ...Yeah, farewell.
Condition：Clear Ep. 14: Seraphina's Secret. A girl in love is invincible!!!
Condition：Clear Ep. 15: The Ultimate Skill. Excellent...
Condition：Clear Final Ep.: Dedicated to the Precious People. I'll save her, no matter what!
Condition：Enter the Carnage Dimension. We can't lose to the overwhelming power of Carnage!
Condition：Conquer the Carnage Dimension. (Defeat Carnage Dark) This is the ultimate power!
Condition：Jump 1,000 times at the base. Once you hop, you just can't stop.
Condition：Hit allies inside the base 100 times. Be gentle.
Condition：Reach the goal in the Chara Word. Congratulations!
Condition：Force the Dark Assembly to approve a bill. In the end, it's all about the "Aye."
Condition：Completely fill the Bonus Gauge. Take everything!
Condition：Complete 20 quests. We'll accept any quest.
Condition：Repel a Netherworld in the Item World. Just another day for you and me in the Netherworld.
Condition：Call your Netherworld for the first time If you call it...it will come.
Condition：Pass a bill that gives you a trophy. Yes, you earned it.
Condition：Nullify all Geo Panels with a Geo Chain of 5 or more. Find the trick and erase all of them at once!
Condition：Pass a bill by Paying Up 100,000,000 HL. I hope it's worth it!
Condition：Get a Game Over. Let this humiliation fuel your strength.
Condition：Experience the effects of the hot springs in an Item World Mystery Room. No peeking on the girls' side.
Condition：Capture 100 prisoners. Round them up!
Condition：Achieve a population of 100 in the pocket Netherworld. The pocket Netherworld has gotten pretty crowded.
Condition：Discover 100 Netherworlds. Find new frontiers!
Condition：Eat curry for 100 days straight. They're demons so they're fine. Please don't try this at home.
Condition：Watch 20 skits. Enjoy the daily lives of demons.
Condition：Use an Overload skill for the first time. Watch closely for the power of an Overlord.
Condition：Perform a Team Attack for the first time. This is the power of bonds!
Condition：Activate Revenge Mode 100 times Your hatred makes you powerful!
Condition：Perform 20 combos. Finish 'em off all at once!
Condition：Get 50 One Time Bonuses. You're taking all the bonuses!
Condition：Unlock all character classes. Master every path possible!
Condition：Obtain more than 10,000,000,000 HL. So, whatcha gonna blow it all on?
Condition：Max out an item's level. Annihilate enemies with the weapons you've modified!
Condition：Reach the goal in the Chara World on Super Overlord difficulty. It takes a lot of gaming to get this far.
Condition：Defeat Proto Darkdeath in the Item World. Wh-Who is this guy...!?
Condition：Obtain an epic item. This is sweet!
Condition：Obtain the legendary weapon in the Item World. Only the chosen one can equip it...
Condition:Level up to Lv 9999. It's just a destination, not the final stop!
Condition：Deal over 10,000,000,000 damage. Blow 'em away!