Carefully drop the columns so that you can release some of the line blasters (by matching beside them) and start removing the metal cages.
Your aim is to set off each line blaster so it will blast away as many cages as it can (try not to also remove another line blaster at the same time!)
Slowly work your way down blasting whole rows of cages.
It is ok if a few wooden ones are left as they can be broken at the bottom.
There is also a bomb near the bottom (handy for both removing cages and releasing pets from their carriers)
You will also build up a rocket on the way down that can help with one column.