Here is the full list of all 51 DmC Devil May Cry: Definitive Edition trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Collect all DmC Devil May Cry™: Definitive Edition Trophies
Complete Vergil's downfall on Vergil Must Die difficulty
Free all of the Lost Souls in Vergil's story
Be awarded a SSS rank on 5 different missions with Vergil
Purchase all of Vergil's combat upgrades
Upgrade Vergil's Devil Trigger to maximum
Kill 1000 enemies with Vergil
Complete all missions (Nephilim or above) on Hardcore mode with Vergil
Complete Vergil's downfall on Son of Sparda difficulty
Upgrade Vergil's health to maximum
Reach wave 30 on Bloody Palace with Vergil
Purchase all of Dante's combat upgrades
Be awarded a SSS rank on 10 different missions with Dante
Complete a mission with a SSS rank
Complete all missions on the Dante Must Die difficulty with Dante
Free all of the Lost Souls in Dante's story
Complete all of the Secret Missions
Upgrade Dante's health to maximum
Upgrade Dante's Devil Trigger to maximum
Slay 2,500 Demons as Dante
Reach wave 50 on Bloody Palace with Dante
Complete all missions on the Son of Sparda difficulty with Dante
Complete all missions (on Nephilim or above) on Hardcore mode with Dante
Spend 20,000 Red Orbs as Dante
Complete 10 Secret Missions
Slay 1,000 Demons as Dante
During "Found", kill 10 enemies using the Hurricane ride
Complete Vergil's downfall
Defeat an Imprisoner
Defeat a Wisp
Complete Dante's story
Defeat Mundus
Help Vergil open the Vault
Acquire Kablooey
During "The Plan", kill all of the enemies before entering the tower
Complete a level without taking any damage
Defeat Mundus' spawn
Acquire Revenant
Acquire Aquila
Acquire Dante's Devil Trigger ability
Help Phineas retrieve his eye
Acquire Eryx
Finish "Secret Ingredient" while killing all of the enemies during the descent
Survive the encounter with the Tyrant in the church
Acquire the Angel Boost ability
Acquire Osiris
Slay 100 Demons as Dante
Acquire Arbiter
Defeat Dante's pursuer
Gain a SSS Style Rank during combat
Purchase Dante's first upgrade