The difficulty with this level is that the pets are in carriers, and only a few blocks drop in the same color.
These correct colored blocks have mesh and metal, so need two hits (matches beside them) to be able to be used.
One carrier (containing a pet) can be in each section of the game at a time, so you could be working on dropping three pets at any one time, but that can get tricky!
The technique used in the example of this video, was to choose one section to drop the pets in.
Notice the one block high gaps in the game? This gap is deliberately to the left of where pets were chosen to fall.
More pets will not drop into each section until it is free of a pet or carrier, but these gaps do not count.
The pets can slide in under here in the carriers when the gap is cleared, and then another is able to fall in the same section so both can be matched together.
Use this method, and the built up paint brushes to get the pets out and rescued!
The paint is handy for joining a carrier and the correct color blocks, or for painting groups to drop the pets more efficiently.