Here is the full list of all 43 Sword Art Online: Lost Song achievements.
Reach the story chapter "The Youthful Goddess."
Complete your first side quest.
Defeat 5 or more enemies at the same time with a single attack.
Reach the story chapter "The World of the Black Fairies."
Reach the story chapter "Fairies in the Sky."
Log into ALfheim Online.
Earn all trophies. "You are an excellent fighter. The best I have ever seen."
Reach the story chapter "The Red-head in the Shadows."
Reach the story chapter "A Paradox of Light and Darkness."
Reach the story chapter "Battle of the Knights of the Tri-blade."
Reach the story chapter "Lies."
Reach the story chapter "Intertwined Desires."
Reach the story chapter "The Dark World."
Reach the story chapter "The Twilight of the Gods."
Reach the story chapter "The Two Idols."
Complete all main story chapters. "We still have a lot more gaming left to do!"
Complete Asuna's side story. "Stay with me forever, Asuna."
Complete Leafa's side story. "I hope that I'll always get along with Sugu."
Complete Silica's side story. "I won't tell anyone what happened here today."
Complete Lisbeth's side story. "We're going to forge a lot of memories together, whether you like it or not."
Complete Sinon's side story. "Sinon is an indispensable part of this team, and an important friend."
Go to the festival with all the game's heroines. "This's a sweet scoop!"
Befriend Sumeragi.
Complete a total of 100 side quests.
Complete a total of 100 Extra Quests and/or Multiplayer Quests.
Complete a side quest, Extra Quest, or Multiplayer Quest with a party consisting of Kirito and Asuna.
Complete a side quest, Extra Quest, or Multiplayer quest with a party consisting of Kirito, Klein, and Agil.
Complete a side quest, Extra Quest, or Multiplayer Quest with a party consisting of Silica, Lisbeth, and Leafa.
Complete a total of 10 side quests, Extra Quests, and/or Multiplayer Quests with a party consisting of any single character.
Complete an Extra Quest without taking damage.
Have the character you are controlling reach 0 HP and become a Remain Light.
Resurrect a party member who has become a Remain Light.
Collect 100 different weapons, not including shields.
Collect 50 different accessories.
Raise a weapon's Enhancement Level to its maximum.
Raise a single Sword Skill to level 500. *OSS included.
Raise a single Magic Skill or Special Skill to level 500.
Raise Asuna, Yuuki, Rain, and Sumeragi's OSS to level 100.
Learn every possible Sword Skill, Magic Skill, and Special Skill for a single character.
Have more than 1,000,000 Yuld.
Defeat 1,000 enemies over the course of the game.
Obtain Excalibur.
Create a party that includes your own custom character.