Here is the full list of all 42 Devil May Cry 4 Special Edition achievements.
Defeat 100 enemies.
Complete a Stylish Rank S (Smokin'!) combo.
Complete a Stylish Rank SS (Smokin' Style!!) combo.
Complete a Stylish Rank SSS (Smokin' Sick Style!!!) combo.
Clear all missions in Human Mode.
Clear all missions in Devil Hunter Mode.
Clear all missions in Son of Sparda Mode.
Clear all missions in Dante Must Die Mode.
Clear all missions in Heaven or Hell Mode.
Clear all missions in Hell and Hell Mode.
Clear all game modes.
Clear all missions in Human Mode with an S ranking.
Clear all missions in Devil Hunter Mode with an S ranking.
Clear all missions in Son of Sparda Mode with an S ranking.
Clear all missions in Dante Must Die Mode with an S ranking.
Clear all secret missions.
Acquire all of Nero's skills.
Acquire all of Dante's skills.
Clear all Bloody Palace Mode stages with an S ranking.
Defeat 1,000 enemies.
Clear all missions in Legendary Dark Knight Mode.
Clear all missions in Legendary Dark Knight Mode with an S Ranking.
Clear the game with Vergil.
Clear the game with Lady and Trish.
Clear all Bloody Palace stages with Nero.
Clear all Bloody Palace stages with Dante.
Clear all Bloody Palace stages with Vergil.
Clear all Bloody Palace stages with Lady.
Clear all Bloody Palace stages with Trish.
Clear all Bloody Palace stages with all characters.
Clear the Bloody Palace within 2 hours.
Defeat Dante in the Bloody Palace without taking any damage.
Clear the Bloody Palace in Turbo Mode.
Defeat Dante with an SSS ranking in Son of Sparda Mode or higher.
Defeat Berial 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 Echidna 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 Angelo Agnus with an SSS ranking in Son of Sparda Mode or higher.
Defeat The Savior with an SSS ranking in Son of Sparda Mode or higher.
Defeat 10,000 enemies.
Defeat 10 enemies within 1 second.