Here is the full list of all 22 Cute Dogs achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Woof!
Complete Level 10 with any time
Complete Level 10 very fast
Complete Level 09 with any time
Complete Level 09 very fast
Complete Level 08 with any time
Complete Level 08 very fast
Complete Level 07 with any time
Complete Level 07 very fast
Complete Level 06 with any time
Complete Level 06 very fast
Complete Level 05 with any time
Complete Level 05 very fast
KuKo
Complete Level 04 with any time
Complete Level 04 very fast
Complete Level 03 with any time
Complete Level 03 very fast
Complete Level 02 with any time
Complete Level 02 very fast
Complete Level 01 very fast
Complete Level 01 with any time