Here is the full list of all 92 NetHack: Legacy achievements.
Play as an Archeologist.
Play as a Barbarian.
Play as a Caveman/Cavewoman.
Play as a Healer.
Play as a Knight.
Play as a Monk.
Play as a Priest/Priestess.
Play as a Ranger.
Play as a Rogue.
Play as a Samurai.
Play as a Tourist.
Play as a Valkyrie.
Play as a Wizard.
Play as every role.
Beat the game.
Beat the game as an Archeologist.
Beat the game as a Barbarian
Beat the game as a Caveman/Cavewoman.
Beat the game as a Healer.
Beat the game as a Knight.
Beat the game as a Monk.
Beat the game as a Priest/Priestess.
Beat the game as a Ranger.
Beat the game as a Rogue.
Beat the game as a Samurai.
Beat the game as a Tourist.
Beat the game as a Valkyrie.
Beat the game as a Wizard.
Beat the game as every role.
Beat the game without eating.
Beat the game as a vegan.
Beat the game as a vegetarian.
Beat the game as an atheist.
Beat the game without using a melee weapon.
Beat the game as a pacifist.
Beat the game without reading or writing anything.
Beat the game without wishing.
Beat the game without genociding.
Beat the game without polymorphing objects.
Beat the game without polymorping yourself.
Beat the game permenantly blind.
Beat the game without wearing any armor.
Beat the game without using Elbereth.
Beat the game adhering to each conduct.
Got all the ascension achievements.
Beat the Archeologist quest.
Beat the Barbarian quest.
Beat the Caveman/Cavewoman quest.
Beat the Healer quest.
Beat the Knight quest.
Beat the Monk quest.
Beat the Priest quest.
Beat the Ranger quest.
Beat the Rogue quest.
Beat the Samurai quest.
Beat the Tourist quest.
Beat the Valkyrie quest.
Beat the Wizard quest.
Beat the quest of every role.
Found the Gnomish Mines.
Found Minetown.
Beat the first level of Sokoban.
Beat the second level of Sokoban.
Beat the third level of Sokoban.
Beat the final level of Sokoban.
Found the Astral Plane.
Found the Plane of Water.
Found the Plane of Fire.
Found the Plane of Earth.
Found the Air Plane.
Found the Oracle.
Found a Big Room.
Found Fort Ludios.
Found the original rogue throwback level.
Found the Flooded Ruins.
Found the Castle.
Found Gehennom.
Found the Valley of the Dead.
Found the Wizard's Tower.
Found Vlad's Tower.
Found the Swamp.
Solved the Castle Drawbridge puzzle.
Be crowned by your deity.
Cheated at Sokoban.
Found the Halls of Wrath.
Found the Chamber of Flies.
Found the Ghost Town.
Find an anthole.
Find a beehive.
Found a throne room.
Took a selfie.
Performed the Invocation Ritual.