There are many special achievements in The Lake House, and "Petting the Cat" is one of them. To unlock it, go to the [Find the Cat] level. Once you arrive, you can easily find the cat. Simply click on its head until Rustie runs away to complete the achievement.
How to Unlock the Petting the Cat Achievement in Rusty Lake: The Lake House
Petting the Cat
Petting the Cat
In the [Find the Cat] level, after finding the cat, click on its head until Rustie runs away.
Related Guide: How to Unlock the Rat Control Achievement in The Lake House