Here is the full list of all 22 BirdGut achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Obtain the escape ending
Obtain the launch ending
Recieve the Blessing of the Nine
Obtain the launch and escape ending
Discover the Skull of the Ninth
Reach the Missile Chamber
Discover the Skull of the Eighth
Reach the colon
Discover the Skull of the Seventh
Reach the large intestines
Discover the Skull of the Sixth
Reach the small intestines
Discover the Skull of the Fifth
Reach the Acid Ocean
Discover the Skull of the Fourth
Reach the stomach city's upper zone
Discover the Skull of the Third
Reach the stomach city
Discover the Skull of the Second
Reach the stomach of the bird
Discover the Skull of the First
Get eaten by the bird.