This can be done in Chapter 3.
Go to 30,26. On the left there are 2 walls hanging from the ceiling. Turn into a ball (R1) between them and grab the right wall. From here jump to the small ledge on the left wall. There’s a hidden path. Follow the path which will lead you to the bird.
Credit to: http://www.ps3trophies.org/game/knytt-underground/guide/
Credit to Mr Vuule for the video