Here is the full list of all 40 Wings of Vi achievements.
Defeat the Ancient Constructs.
Defeat Terravine with at least one minecart left in the room.
Defeat the Dark Annihilator without letting any bombs touch the floor.
Travel below each platform during the first minecart sequence.
Defeat Myougi without taking any damage.
Defeat Kratarac.
Defeat Amethyst.
Defeat Terravine.
Reach the upper platform in the underwater area in Sinister Grotto.
Read all the stories in the Floating Keep library.
Defeat the Dark Annihilator.
Defeat Electram.
Defeat Pr'Gora.
Find a secret.
Defeat Myougi.
Defeat Myougi having done maximum damage to her each time she deactivates her shield (4 damage).
Beat Rubi in the obstacle course race.
Make all the birds in Vi's home fly away.
Watch over the broken bridge.
Defeat Pr'Gora without taking any damage.
Defeat Electram without taking any damage.
Defeat Amethyst without taking any damage.
Talk to a person who hid themself in the caves.
Defeat the Dark Annihilator without taking any damage.
Beat the last segment in the Sinister Grotto while having defeated all spawns of Terravine along the way.
Defeat Terravine without taking any damage.
Defeat Kratarac without taking any damage.
Defeat the Ancient Constructs without taking any damage.
Defeat the Ancient Constructs only enraging one of his three heads.
Defeat Myougi again.
Defeat Myougi again without taking any damage.
Defeat the Twin Orcs.
Defeat the Twin Orcs without taking any damage.
Defeat Azurel.
Defeat Azurel without taking any damage.
Unlock all weapons.
Defeat Jeh'Oul.
Defeat Jeh'Oul without taking any damage.
Defeat Supreme Jeh'Oul and save the world.
Defeat Supreme Jeh'Oul without taking any damage.