Here is the full list of all 43 Devil May Cry 4 Special Edition trophies - there are 32 bronze, 6 silver, 4 gold and 1 platinum.
Acquire all trophies.
Clear all game modes.
Clear all missions in Legendary Dark Knight Mode.
Clear all missions in Legendary Dark Knight Mode with an S Ranking.
Defeat Angelo Agnus with an SSS ranking in Son of Sparda Mode or higher.
Defeat Angelo Credo with an SSS ranking in Son of Sparda Mode or higher.
Clear all missions in Hell and Hell Mode.
Defeat Berial with an SSS ranking in Son of Sparda Mode or higher.
Clear all Bloody Palace stages with Vergil.
Clear all Bloody Palace stages with all characters.
Defeat Dante in the Bloody Palace without taking any damage.
Clear all Bloody Palace stages with Dante.
Defeat 10 enemies within 1 second.
Clear all Bloody Palace stages with Nero.
Defeat The Savior with an SSS ranking in Son of Sparda Mode or higher.
Clear all Bloody Palace stages with Lady.
Defeat 10,000 enemies.
Clear all Bloody Palace Mode stages with an S ranking.
Clear all Bloody Palace stages with Trish.
Clear the Bloody Palace within 2 hours.
Clear the Bloody Palace in Turbo Mode.
Defeat Dante with an SSS ranking in Son of Sparda Mode or higher.
Clear all missions in Dante Must Die Mode with an S ranking.
Clear all missions in Dante Must Die Mode.
Defeat Echidna with an SSS ranking in Son of Sparda Mode or higher.
Clear all missions in Heaven or Hell Mode.
Clear the game with Lady and Trish.
Defeat Bael or Dagon with an SSS ranking in Son of Sparda Mode or higher.
Clear all missions in Son of Sparda Mode with an S ranking.
Clear all missions in Son of Sparda Mode.
Clear all missions in Devil Hunter Mode with an S ranking.
Clear all missions in Devil Hunter Mode.
Clear the game with Vergil.
Clear all secret missions.
Clear all missions in Human Mode with an S ranking.
Clear all missions in Human Mode.
Acquire all of Dante's skills.
Acquire all of Nero's skills.
Complete a Stylish Rank SSS (Smokin' Sick Style!!!) combo.
Defeat 1,000 enemies.
Complete a Stylish Rank SS (Smokin' Style!!) combo.
Complete a Stylish Rank S (Smokin'!) combo.
Defeat 100 enemies.