Choose the column that looks like it has the easiest way down to get your Pet/s.
If you come across a metal block or other obstacle before the Pet falls, then change columns.
Once you find a path down it might help to keep working on that section of the board.
If you get stuck use the rocket booster to drop the Pet, or to drop one of the line blasters.
Using a line blaster can clear a whole bottom row of mis-matched blocks.
Make use of any short columns to the left of the column you're working in, removing a whole (shorter) column can slide everything to the left and bring down a Pet more quickly.