Welcome to the Pet Rescue Community
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Hi @joyjaros each Pet you rescue in a newly played level comes to live in your city!
So to reach 1000 you need to save more pets by playing levels.
Previous levels do not count unless you're at the end of the game and use the 'random levels' button.
The 'sunshine shade' quest is fulfilled by doing exactly as it asks, by putting more hats on your Pets.
Hats are one of the card options you get when you complete a new level.