Golden Egg #13 is located in Level 1-8: Reveal the Golden Egg by hitting the TNT under the slingshot. You can do this by bouncing a red bird off the checkered wall directly under the first concrete block. Now bust that Golden Egg! (→ see image)
Note, this is a two part video. The first part shows how to find the Golden Egg and the second is a walkthrough on how to pass the actual Golden Egg level.