Here is the full list of all 45 Stranger of Sword City trophies - there are 27 bronze, 15 silver, 2 gold and 1 platinum.
Hunted down Le Musa and completed the quest [Poison to Poison].
You have re-hunted a Lineage Type for the first time.
Performed a sacrifice at Monolith and completed the quest [Dimension Gate].
You retrieved Gurrba Panties.
You have been registered as a Chosen One at the Strangers Guild.
You hunted Lineage Type Blue Head.
Performed an evaluation with Armor Knights and completed the quest [Knight Standoff].
You fed Mumic a unique item.
Completed a quest for Gnuta.
You obtained a C rank equipment.
You obtained a D rank equipment.
You obtained an E rank equipment.
You have won 50 ambush battles.
You obtained a B rank equipment.
You have won 20 ambush battles.
You have begun to hunt down the Lineage Types that hide within the labyrinths.
You hunted Lineage Type Mukabu the Third.
Your first time seeing a Butterfly Nest.
You have won an ambush battle.
You have created your own character.
You've got all of the Stranger of Sword City Trophies! Thank you very much for playing!
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 hunted down 10 Lineage Types in one playthrough.
You have hunted down 20 Lineage Types in one playthrough.
You found 10 Butterfly Nests.
You found 30 Butterfly Nests.
You have obtained Small Muramasa.
You have obtained the legendary katana, Muramasa.
You have obtained the mighty giant cursed katana.
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.