To rescue the Pets you'll need to move them to the left and down.
For them to move, whole columns to their left have to be removed.
Columns can be destroyed with the rocket booster (built up within the game), line blasters (that fall), and by having the column all one color blocks, or all the virus blocks, to be matched.
Remember that to remove a whole column with a line blaster or rocket there must be no meshed blocks in the column.
The timed line blasters in this Level can be both a help and a problem! Good Luck.