First arm yourself with infinite lives (these can be won from the bonus games Mystery Mountain and Weather Alert)
When you first open the game look at the butterflies. If you do not have at least three the same color, quit now, you'll never manage to win.
Assuming you now have the game open with at least three of the one color butterfly, carefully build up a group of that color.
Avoid using the balloon as it will waste your blocks and every block is needed in this level!
Only use the balloon when you have sixteen of the correct color.
When you need to get more Pets on the board choose small (two or three block) moves to not waste more valuable blocks.
It takes two moves between saving a Pet and the next one falling.
Once you've almost saved all the Pets this is the time to use some boosters if you have them. Don't waste boosters using them in the beginning of the level.
If all the Pets you need are on the board (even in carriers) you can use the mega bomb won from the Golden Panda.
Otherwise, painting blocks the color you need and/or using balloons to fill the butterfly can also be helpful.