In 2006, Arto Inkala, a professor of applied mathematics in Finland, released a puzzle that he called “Escargot” (from the shape that the numbers formed). He had spent months developing it, and he described it as the most difficult Sudoku ever created. In the years since, other puzzles have been designed that are arguably even more difficult, but Escargot is still significant in Sudoku history. It represents the first appearance of such extremely difficult puzzles, and it remains a benchmark against which to test any solving method.
I approached Escargot the same way that I approached the other puzzles demonstrated here. I marked “only two cells” situations, and when I did, I noticed a concentration of them in the top three blocks. There were a few other such situations scattered throughout the rest of the puzzle, but following the principle of “take what a Sudoku gives you” (or, put another way, “go where the numbers are”), I focused my efforts on those three blocks. (Accordingly I have not marked those other situations in the video.)
The video shows the results of the many challenging but enjoyable hours I spent solving Escargot. It does not show the entire process. When I say at one point that a couple of possible paths led to falsities, I mean that they did so eventually, after much determined solving!
As I say in the comments on Example 3, I think of a "forcing chain" as putting a number in a cell without knowing for certain that it goes there but nevertheless being convinced on the basis of analysis that it would be promising. It was on that basis that I decided where and how to start the forcing chain that ultimately led me to a solution for Escargot.