A Hard 9×9 Puzzle Solved with Forced Chain in 21 Steps

This 9×9 board rates as hard (difficulty score 1015). Solving it from scratch takes 21 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, every open cell left in this region sits in row 9, so its marker has to land there; that clears every other open cell in the row.
2. Next, together, two regions have open cells only in rows 7 and 8; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
3. Then, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
4. After that, together, two regions have open cells only in columns A and B; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
5. Now, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
6. From there, together, two regions have open cells only in columns C and D; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
7. Following that, every remaining candidate in this region touches E2 and F2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
8. First, every remaining candidate in this region touches A8 and B8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
9. Next, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
10. Then, place a marker at B9. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
11. After that, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
12. Now, place a marker at C5. Region has exactly one open cell left.
13. From there, that one can't be the marker: at F1 it would force H2 (the last open cell in region 2), and row 3 would be left with no open cell for its marker.
14. Following that, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
15. First, every open cell in column F belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
16. Next, every remaining candidate in this region touches E3 and G4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
17. Then, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
18. After that, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region. Placing here also clears its 1 touching neighbour.
19. Now, place a marker at I4. Region has exactly one open cell left. Placing here clears the rest of row 4, column I, and its region.
20. From there, place a marker at F3. Region has exactly one open cell left.
21. Finally, place a marker at G6. Region has exactly one open cell left.

The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎