There are 6 available birds on each level. For this achievement, you must find all of them during Chapter 4 during 1 play through. If you complete the stage without finding them all, you must play it again and find all of them over again. If you would like a text guide for the locations of all the birds, and all the other collectibles as well, below is a great guide put together by DarkS0urce of GameFAQS:http://www.gamefaqs.com/console/xbox360/file/926309/40202
P.S. If you are worried about spoilers, don't view the videos, it shows a playthrough of the level from beginning to end while collecting everything.
Videos removed because the user deleted them.