Here is the full list of all 43 Save the Dodos achievements.
Reach 1000000 points overall
Clear 100 levels
Kill 5 dodos at the same time
Win 150 stars
Save 5 dodos at the same time
Complete 35 achievements
Clear 60 levels
Save 200 dodos
Reach 500000 points overall
Get more than 3 special dodos
Lose a dodo next to an exit
Get more than 2 special dodos
Win 50 stars
Save 100 dodos
Save a dodo narrowly
Get more than 1 special dodos
Clear 25 levels
Keep a tile pressed more than 25s
Lose a dodo in less than 1s
Move 15 tiles in less than 5s
Move 10 tiles in less than 5s
Complete 20 achievements
Move 5 tiles in less than 5s
Accelerate time more than 25s
Do nothing during more than 60s
Do nothing during more than 30s
Reach 50 defeats
Reach 25 defeats
Play a level more than 25 times
Kill 100 dodos
Complete 10 achievements
Reach 10 defeats
Play a level more than 10 times
Lose in less than 20s
Kill 50 dodos
Save 50 dodos
Kill 20 dodos
Play a level more than 5 times
Clear a level in less than 20s
Clear a level in less than 15s
Clear a level in less than 25s
Reach 1500000 points overall
Win 300 stars