Firstly, save your balloon, (you'll need it later)
Build up your line blaster booster as soon as possible by clicking large groups of blocks, try to get the two pets on your board rescued while you do this.
Once you have your first line blaster (spring) use it to take the mesh off the bottom block in the central column.
Now you can pop the balloon. This will get things falling in this column, it has bombs and more springs.
Explode any bombs that fall in the center. It will set off springs and clear blocks from that column and make more springs fall, (and if you're lucky balloons will fall to make clearing the blocks easier!)
This level only drops one pet per column at a time.
So to keep the game moving, as soon as a pet has been saved, click away some blocks from the column it just left to open the column up and allow another pet to fall.
This way you can be working on lowering six pets all the time.
It is a difficult level to get the required amount of Pets in the limited number of moves.