This level is all about clever use of your line blasters.
Concentrate on the bottom row.
Match and remove blocks from this row to bring down the vertical line blasters.
Use these line blasters to drop columns of blocks
Once the horizontal line blasters are at the bottom of a column, you can remove that whole column (with a vertical line blaster) and slide the Pet down to the exit
Keep sliding the Pet down, releasing it from the cage at some stage of the journey, until it is free.