Here is the full list of all 42 Devil May Cry 4 Special Edition achievements.
Clear all missions in Hell and Hell Mode.
Clear all game modes.
Clear all Bloody Palace stages with Trish.
Clear all Bloody Palace stages with all characters.
Clear all Bloody Palace stages with Vergil.
Clear all Bloody Palace stages with Lady.
Clear all Bloody Palace stages with Dante.
Defeat Dante in the Bloody Palace without taking any damage.
Clear the Bloody Palace in Turbo Mode.
Clear all Bloody Palace Mode stages with an S ranking.
Clear all Bloody Palace stages with Nero.
Clear the Bloody Palace within 2 hours.
Clear all missions in Heaven or Hell Mode.
Clear the game with Lady and Trish.
Defeat 10,000 enemies.
Clear all missions in Dante Must Die Mode with an S ranking.
Defeat The Savior with an SSS ranking in Son of Sparda Mode or higher.
Clear all missions in Dante Must Die Mode.
Clear all missions in Legendary Dark Knight Mode with an S Ranking.
Clear all missions in Legendary Dark Knight Mode.
Clear the game with Vergil.
Clear all secret missions.
Defeat Dante with an SSS ranking in Son of Sparda Mode or higher.
Clear all missions in Son of Sparda Mode.
Clear all missions in Son of Sparda 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.
Defeat Echidna with an SSS ranking in Son of Sparda Mode or higher.
Defeat Bael or Dagon with an SSS ranking in Son of Sparda Mode or higher.
Defeat Berial with an SSS ranking in Son of Sparda Mode or higher.
Clear all missions in Devil Hunter Mode.
Clear all missions in Devil Hunter Mode with an S ranking.
Defeat 10 enemies within 1 second.
Acquire all of Dante's skills.
Clear all missions in Human Mode with an S ranking.
Clear all missions in Human Mode.
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.