Extremely difficult grids are not easy to find. I only encountered 18 grids. Since I wanted to have an endless supply of grids to play with, I experimented with transformations until I had the possibility of 1M+ extremely difficult grids -- obviously many would be uninteresting or repetitive schematically, but there is plenty of room for imagination.
Extremely difficult grids all have 2 empty rows & 2 empty columns. The following grids represent: a butterfly, a happy face, a fountain & a double oval.