First drop the metal boxes and line blaster (spring) down the board.
Try to not keep the metal boxes all in a row, if they are staggered you can paint between or under some of them with the paint that comes within this game.
If you're lucky you can get them all into the bottom row, lined up with the line blaster.
Some of the block busters (hammers) that can be bought (on PC versions of the game) with your free Pet Rescue Coins can be very handy to even things out, but it is also possible without as shown in the video example.
Blast away as many of the metal boxes as you can, the others can be brought down with the rocket boosters you'll build up within the game.
Use your paint to make large groups of blocks, it is great if you have more than one can of paint in the same color.
These large groups will build up your booster quickly and drop the pets more efficiently.
Five Pets seems to be the maximum you can have on your board at a time, so try to always be working on bringing 5 down.