Here is the full list of all 24 Bastion achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Complete the story, embracing the New World
Complete the story in New Game Plus
Complete 100 percent of the Vigils in the Memorial
Use the Forge to fully upgrade every weapon.
Complete each trip to Who Knows Where
Get four different domesticated creatures in the Bastion
Use the Skyway in the Wharf District.
Complete the story
Use the Forge to apply at least one upgrade to every weapon
Complete at least 50 percent of the Vigils in the Memorial
Stop the siege on the Bastion
Complete Prosper Bluff and speak with the Singer in the Bastion
Complete the Hanging Gardens and speak with the Survivor in the Bastion
Complete the Wharf District
Defeat the required number of foes using a single Turret.
Complete the Kid's Dream with five or more Shrine Idols invoked.
Complete the Kid's Dream with all ten Shrine Idols invoked.
Complete the Singer's Dream with five or more Shrine Idols invoked.
Complete the Singer's Dream with all ten Shrine Idols invoked.
Complete the Survivor's Dream with five or more Shrine Idols invoked.
Complete the Survivor's Dream with all ten Shrine Idols invoked.
Earn a total of at least 1,000,000 points in Score Attack Mode
Complete the Stranger's Dream with five or more Shrine Idols invoked.
Complete the Stranger's Dream with all ten Shrine Idols invoked.