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