Here is the full list of all 215 JQ: dogs & cats achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Abyssinian
Ethiopia
Minskin
Toyger
Manx
Isle Of Man
Maine Coon
Bengal cat
Siberian
Somali
British Shorthair
Norwegian Forest
Norway
Sokoke
Kenya
Ukraine
Ukrainian Levkoy
Havana Brown
Thailand
Korat
Scottish Straight
American
Savannah
Chartreux
Nebelung
Egypt
Egyptian Mau
German Rex
Russian Blue
Munchkin
Donskoy
Japanese Bobtail
Persian
Iran
Tonkinese
USA
Start Cats
Alabai
Komondor
Hungary
Briard
Italian Greyhound
Italy
German Shepherd
Poodle
France
Rottweiler
Dachshund
Newfoundland
Pekingese
Dobermann
Shih Tzu
Chow Chow
Husky
Russia
Basenji
Democratic Republic of the Congo
Bull Terrier
Weimaraner
Germany
Chihuahua
Mexico
Irish Setter
Ireland
Pug
Caucasian Shepherd Dog
USSR
Shetland Sheepdog
Scotland
Czechoslovakian Wolfdog
Czech Republic
Tibetan Mastiff
English Bulldog
England
Shar Pei
China
Akita-inu
Japan
Dalmatian
Croatia
Afghan hound
Canada
Wales
Great Britain
Switzerland
Afghanistan
Labrador
Welsh Corgi
St. Bernard
Greyhound
Berner Sennenhund
EmiSoter
Start Game