Here is the full list of all 12 Arctictopia achievements.
Complete the first level.
Meet the seal for the first time.
Meet the puffin for the first time.
The first setback.
Yes, you have completed all levels!
Onwards! To the unknown parts of the world!
Who's a good dog, huh? Who's the BEST dog?
Unlock the first map area.
Unlock the second map area.
Unlock the third map area.
Unlock the fourth map area.
Unlock the fifth map area.