To complete Level 729 you first need to have the correct number of line blasters drop within the game!
If none have fallen within the first ten moves, give up, quit and try again (at least then you only waste a Pet Rescue life and not time out of your real life)
The four places you need to destroy with a line blaster are the metal covered blocks in the first column.
The bottom block needs two blasts and the third block up needs just one, the other mesh covered blocks can be cleared with matches next to them.
You also need one to wipe away a whole column so that it will slide across and give you blocks to work on clearing the end, right column.
Sliding a column will only work if the line blaster is at the very top row, or right down on the bottom row.
Try to make all the blasts you need before you clear the columns with pets, because basically if you don't get these four blasts, the game is unable to be completed anyway.
Once the right column has had three blasts, clear it from the bottom up.
Then use matches to clear the other column that has a pet.
If you are really lucky more line blasters could fall to help you, but with the limited moves and the random nature of the line blasters, this is unlikely!