Here is the full list of all 36 Harmony's Odyssey achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
Get Cerberus mad
Take a look at the city rogues
Discover Olymp Estate
Unlock Detective Mummy Part 2 mini game
Discover Harmony's home
Unlock Cat's Delivery Service mini game
Unlock Detective Mummy mini game
Unlock Detective Mummy Part 3 mini game
Unlock Bull's Football League mini game
Unlock Werestorms Attack mini game
Unlock Dungeons'n'Mice mini game
Complete all Cat's Delivery Service levels
Complete all Bull's Football League levels
Recover cat's memories
Recover all missing cat parts
Fly through the mythical ocean
Get Minotaur mad
Get Cyclops mad
Get Detective Mummy angry
Make Odin really angry
Do cats even like sausages?
Help Dragonmice escape
Get Cyclops a winter treat
Discover Bull's Football Field
Discover the Airport
Discover Winter Resort
Spend some time behind bars
Complete the campaign
Complete all arcade mode levels
Discover the family collection
Spend your first earned star
Discover the arcade room
Visit the Audio Room in Home Hub
Finished a level in over 25 minutes
Complete all levels on Hard difficulty
Complete all Puzzle levels