Here is the full list of unlockable achievements for Bastion on the Xbox 360.
Altruist (20) – Complete 100 percent of the Vigils in the Memorial
Calamity Kid (30) – Complete the story in New Game Plus
Kid-at-Arms (10) – Use the Forge to apply at least one upgrade to every weapon
Mind Voyager (20) – Complete each trip to Who Knows Where
Pet Sitter (10) – Get four different domesticated creatures in the Bastion
The End (20) – Complete the story
The Stranger (10) – Complete the Wharf District
Vigilante (10) – Complete at least 50 percent of the Vigils in the Memorial
And here are the four secret achievements you can unlock in the game:
The Beginning (20) – Complete the story, embracing the New World
The Singer (20) – Complete Prosper Bluff and speak with the Singer in the Bastion
The Survivor (10) – Complete the Hanging Gardens and speak with the Survivor in the Bastion
The Ura (20) – Stop the siege on the Bastion