This level is very difficult to complete booster free!
To achieve it you need to find a balance between using the paint and saving moves by working without it.
Use the paint to create large groups of blocks to both build up the mesh masher booster, and bring the Pets down.
The mesh masher makes the board clearer and easier to paint.
Notice the first move in this game can also slide all the columns to the left and immediately save one Pet, effectively giving you a total of only 11 to bring down.
Only three Pets will ever be on the board at a time.
When one is saved, if you can, choose the column that looks easiest to get it down and click that column.
It can also help to concentrate on one side of the game at first.
Then half way through, when the mesh has built up on the side you're on, move to the other side, which is hopefully clearer.