Here are the four secret achievements you can unlock in the Bastion for the Xbox 360.
Check out my other guide if you are looking for the full list of unlockable achievements in Bastion.
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