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