Here is the full list of all 44 Stranger of Sword City achievements.
You have won 50 ambush battles.
You have hunted down your first Lineage Type twice.
Performed a sacrifice at Monolith and completed the quest [Dimension Gate].
Hunted down Le Musa and completed the quest [Poison to Poison].
Performed an evaluation with Armor Knights and completed the quest [Knight Standoff].
You hunted Lineage Type Blue Head.
Completed a quest for Gnuta.
You have won 20 ambush battles.
You have begun to hunt down the Lineage Type that hides within the labyrinth.
You hunted Lineage Type Mukabu the Third.
Your first time seeing a Butterfly Nest.
You obtained a C rank equipment.
You obtained a B rank equipment.
You obtained a D rank equipment.
You have won an ambush battle.
You have created your own character.
You have been registered as the Chosen One at the Strangers Guild.
You obtained an E rank equipment.
Hunted down Death Dragon and completed the quest [Elder's Suggestion].
Completed a quest for the Phoenix Brother Squad and completed the quest [Phoenix Squad].
Traveled through the Valley of the Ruined and completed the quest [Call From Kyo].
Completed the quest [Sudden Departure].
Reached the deepest end of the sea and discovered Marilith's secrets.
Escaped from the Elder's evil clutches and completed the quest [Land of the Origin].
Found out the truth from Dranserk at the Mausoleum of Ice.
Hunted Charon and completed the quest [Mausoleum of Storms].
Hunted down Kyo, who ambushed the guild.
Reached the end of the story.
Finished the Dragon God's challenge and unleashed yourself from the chains of destiny.
You have re-hunted down 10 Lineage Types in one playthrough.
You have re-hunted down 20 Lineage Types in one playthrough.
You found 10 Butterfly Nests.
You found 30 Butterfly Nests.
You fed Mumic a unique item.
You have obtained Small Muramasa.
You have obtained the legendary katana, Muramasa.
You have obtained the mighty giant cursed katana.
You retrieved Gurrba Panties.
You retrieved Anna's Undies.
You obtained an A rank equipment.
You obtained an S rank equipment.
You hunted Lineage Type Ghost Captain.
You hunted Lineage Type Jormungand.
You hunted Lineage Type Tri-color.