Here is the full list of all 40 Accel World VS Sword Art Online Deluxe Edition achievements.
Obtained all achievements.
Cleared a Challenge Quest.
Completed all of Hexe's requests.
Destroyed a solid Otherworld object.
Acquired 100 total titles.
Started episode 5 of "Say It, Miss Strea!"
Unlocked Nitride Unica.
Raised a weapon from Rank 1 to Rank 10.
Cleared 50 quests.
Cleared every "Navigation" episode.
Received 50 titles.
Unlocked all seven Kings.
Obtained 100 different types of equipment.
Cleared "Timeless Bonds."
Cleared every "Mystification" episode.
Unlocked Seven.
Cleared "Millennium Twilight."
Cleared "A Gleam of Hope."
Cleared "Lost Wish, Tumultuous Heart."
Cleared "Showdown."
Cleared an Extra Quest with only Sky Raker, Ardor Maiden, and Aqua Current.
Cleared an Extra Quest with only Asuna and Black Lotus.
Cleared an Extra Quest with only Kirito and Silver Crow.
Raised one character's level to 1000.
Cleared "Disastrous Moonlight."
Raised one character's level to 500.
Cleared "Cold Trap."
Used BP to buy something.
Chained together 8 skills with Skill Connect.
Cleared "The Impatient Skies."
Cleared an Extra Quest.
Enhanced one weapon to +10.
Cleared a Sudden Quest.
Raised one AW character's skill level to 500.
Raised one SAO character's skill level to 500.
Cleared a Friend Quest.
Performed a Switch.
Employed a blacksmith's services.
Cleared "The Invader."
Defeated the aura-clad monster general.