To pass level 852 it is great if you can start with a board that has large group/s of the one color.
You need these to build up the booster and swipe the crates as quickly as possible.
Try not to move the middle two columns down too soon and not to do them individually (keep them level), as this seems to cause a metal block to drop and makes the level a whole lot harder with one more obstacle to destroy.
Clear the mesh and metal off the bottom blocks and drop the pets down, at the same time move the two balloons to the bottom to break their glass.
Use a balloon to free one pet, then free the other two. If you also have a metal block to destroy line it up with the remaining pet carrier to swipe with the next line blaster you build up.
The wooden crates will smash when they hit the ground.
Once all the obstacles are gone, hopefully you will still have enough moves to bring the pets down.