Here is the full list of all 40 Accel World vs. Sword Art Online trophies - there are 26 bronze, 10 silver, 3 gold and 1 platinum.
Obtained all trophies.
Acquired 100 total titles.
Raised a weapon from Rank 1 to Rank 10.
Raised one AW character's skill level to 500.
Raised one character's level to 1000.
Enhanced one weapon to +10.
Received 50 titles.
Raised one SAO character's skill level to 500.
Completed all of Hexe's requests.
Unlocked all seven Kings.
Raised one character's level to 500.
Destroyed a solid Otherworld object.
Cleared every "Mystification" episode.
Chained together 8 skills with Skill Connect.
Cleared every "Navigation" episode.
Obtained 100 different types of equipment.
Cleared 50 quests.
Cleared an Extra Quest with only Sky Raker, Ardor Maiden, and Aqua Current.
Unlocked Nitride Unica.
Cleared "Timeless Bonds."
Started episode 5 of "Say It, Miss Strea!"
Unlocked Seven.
Cleared "Millennium Twilight."
Cleared "A Gleam of Hope."
Cleared "Lost Wish, Tumultuous Heart."
Cleared "Showdown."
Cleared "Disastrous Moonlight."
Cleared an Extra Quest with only Asuna and Black Lotus.
Cleared an Extra Quest with only Kirito and Silver Crow.
Cleared "Cold Trap."
Used BP to buy something.
Employed a blacksmith's services.
Cleared a Challenge Quest.
Cleared "The Impatient Skies."
Cleared an Extra Quest.
Cleared a Sudden Quest.
Cleared a Friend Quest.
Cleared "The Invader."
Defeated the aura-clad monster general.
Performed a Switch.