Here is the full list of all 15 Pet idle achievements.
One of your pets has reached level 25!
One of your pets has reached level 50!
One of your pets has reached level 100!
You have become a beginner pet caretaker!
You have become an amateur pet caretaker!
You have become a professional pet caretaker!
Congratulations! You won the trophy for having 2 pets!
Congratulations! You won the trophy for having 4 pets!
Congratulations! You won the trophy for having 8 pets!
Congratulations! You have accumulated the fortune of 100.000 coins!
Congratulations! You have accumulated the fortune of 500.000 coins!
Congratulations! You have accumulated the fortune of 1.000.000 coins!
Congratulations! Your house has reached the Medium House mark!
Congratulations! Your house has reached the Big House mark!
Congratulations! Your house has reached the Huge House mark!