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.
Raised one character's level to 500.
Unlocked Nitride Unica.
Cleared every "Mystification" episode.
Cleared every "Navigation" episode.
Unlocked Seven.
Started episode 5 of "Say It, Miss Strea!"
Cleared "Timeless Bonds."
Cleared "Millennium Twilight."
Cleared "A Gleam of Hope."
Cleared "Lost Wish, Tumultuous Heart."
Destroyed a solid Otherworld object.
Cleared "Showdown."
Obtained 100 different types of equipment.
Cleared an Extra Quest with only Sky Raker, Ardor Maiden, and Aqua Current.
Chained together 8 skills with Skill Connect.
Cleared 50 quests.
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.
Cleared "The Impatient Skies."
Cleared an Extra Quest.
Employed a blacksmith's services.
Cleared a Sudden Quest.
Cleared a Friend Quest.
Cleared a Challenge Quest.
Cleared "The Invader."
Defeated the aura-clad monster general.
Performed a Switch.
Obtained all trophies.
Completed all of Hexe's requests.
Raised one character's level to 1000.
Raised one SAO character's skill level to 500.
Raised one AW character's skill level to 500.
Enhanced one weapon to +10.
Raised a weapon from Rank 1 to Rank 10.
Received 50 titles.
Acquired 100 total titles.
Unlocked all seven Kings.