Here is the full list of all 12 Snakebird Primer achievements.
Complete all levels
Complete all levels on the Desert area
Complete all levels on the Ruin area
Complete the Final level
Complete all levels on the Space area
Complete all levels on the Temple area
Complete all levels on the Ocean area
Complete all levels on the Winter area
Eat fruit
Complete all levels on the Jungle area
Kill birds
Complete all levels on the Island area