Here is the full list of all 10 My Universe - there are Puppies & Kittens achievements.
Adopt your first furry friend.
One of your furry friends gains a friendship level.
One of your furry friends reaches level 10.
Rub the belly of one of your fluffy puppies.
Satisfy every need of a pet.
Have 4 puppies in your living room.
Take your pet on 50 walks. Who wouldn't walk 500 miles for their pets?
One of your lovely kittens reaches level 10.
Have your kittens tackle 50 objects in the laser pointer minigame.
Collect 99 999 trainer points.