This is one of those levels that requires both luck and skill.
It helps very much if you start with a large group of blocks on the board that is the correct color for your butterfly.
If you do not start with a board from which you can fill the butterfly in one or two moves, it is better not to waste your time playing, just quit and try again!
After you've saved a Pet try to make some small moves of only two or three blocks.
This way, you're not wasting big groups that can fill a butterfly, or make the blocks run out before all the Pets are collected.
During these small moves a new Butterfly will drop.
Now concentrate on getting enough blocks in a few moves to free the next butterfly.
Use the in game paint booster to help join the right color blocks, or double the score of some of the right color blocks.
Continue doing these steps until all the Pets are rescued. (Or you run out of matches and need to start all over again!)