Instructions
Use the left or right bumpers to open the "Social" tab on the Xbox dashboard.
Select your own avatar from your friends list and press "A."
Move the cursor right to highlight "Achievements" and press "A."
Scroll through the list of games you've played to find the one with the achievement you want to share. Select it and press "A."
Use the arrows to highlight the icon for the achievement you want to share and press "X."
Select "Add Message," press "A" and type a message using the onscreen keyboard if you want to submit text along with your achievement notice.
Select "Share" and press "A" to send the achievement to Facebook. After the upload finishes, you can return and select additional achievements to share if you want to.