This is the most efficient way I've found to complete this Level, but not the only way!
First, drop the pets so that they are within the bottom six rows (opposite the line blasters) try to clear the metal and mesh from the bottom two rows while you do this.
When you build up the first rocket booster save it until the line blasters in the first column are facing right, then shoot it up them.
Now most of the pets will be at the bottom of their columns.
Concentrate on the line blasters in the game and use those in the bottom row to clear the Pets.
Every three moves set one off to clear a column and bring the Pet in it down.
In between these moves clear the mesh off all the blocks in the columns to the left of each of the remaining Pets and bring any Pets that need it down to the bottom row.
Use the built up in-game rocket boosters to clear these columns, the Pet will the slide to the left and be free.
Remember that columns will only slide if they can be cleared completely, so this means no mesh can be in them and the Pet needs to be at the bottom of the column, ready to go!