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

This 9×9 board rates as hard (difficulty score 1100). 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 remaining candidate in this region touches D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
2. Next, marking A1 would force C2, G2, H2, and 1 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then C3 (the last open cell in region 2), then E5, F5, G5, and 2 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), and the chain continues, and then row 7 would be left with no open cell for its marker. So A1 can't be the marker there.
3. Then, if B1 were the marker, it would force C3 (the last open cell in region 2), then G2, H2 and I2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then E6, E7, E8, and 6 more cleared (together, two regions have open cells only in columns E and F), and the chain continues, and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
4. After that, every remaining candidate in this region touches A3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
5. Now, that one can't be the marker: at C1 it would force A2, G2, H2, and 1 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then B3 (the last open cell in region 1), then D4, D6 and D8 cleared (together, two regions have open cells only in columns A and D), and the chain continues, and region 9 would be left with no open cell for its marker.
6. From there, marking D1 would force F2 (the last open cell in region 3), then B3 (the last open cell in region 1), then E6, E7, E8, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), and then region 9 would be left with no open cell for its marker. So D1 can't be the marker there.
7. Following that, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
8. First, every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
9. Next, together, two regions have open cells only in rows 2 and 3; 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.
10. Then, every remaining candidate in this region touches B2 and B3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
11. After that, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
12. Now, place a marker at C3. Region has exactly one open cell left. Placing here also clears its 2 touching neighbours.
13. From there, 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.
14. Following that, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 1 touching neighbour.
15. First, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
16. Next, place a marker at H6. Region has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region. Placing here also clears its 2 touching neighbours.
17. Then, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
18. After that, place a marker at F9. Region has exactly one open cell left. Placing here clears the rest of row 9, column F, and its region. Placing here also clears its 1 touching neighbour.
19. Now, place a marker at D7. Region has exactly one open cell left.
20. From there, place a marker at I8. Region has exactly one open cell left. Placing here clears the rest of row 8, column I, and its region.
21. Finally, place a marker at G1. Region has exactly one open cell left.

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