How to solve this 8×8 logic puzzle

8×8 · severe · 25 steps

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This 8×8 board rates as severe (difficulty score 1337). Solving it from scratch takes 34 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.

First, every remaining candidate in this region touches G3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Next, every remaining candidate in this region touches B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, marking A1 would force B8 (the last open cell in region 8), then G2 (the last open cell in column G), and then row 3 would be left with no open cell for its marker. So A1 can't be the marker there.
After that, that one can't be the marker: place it at F1, and region 4 would be left with no open cell for its marker.
Now, marking G1 would force F3 (the last open cell in region 4), and then region 2 would be left with no open cell for its marker. So G1 can't be the marker there.
From there, if H1 were the marker, it would force G8 (the last open cell in region 6), then A7 (the last open cell in region 8), then D6 (the last open cell in region 7), and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
Following that, 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.
First, that one can't be the marker: at A2 it would force F3 (the last open cell in region 4), and region 2 would be left with no open cell for its marker.
Next, that one can't be the marker: place it at G2, and region 2 would be left with no open cell for its marker.
Then, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
After that, together, two regions have open cells only in columns H and G; 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.
Now, if E1 were the marker, it would force F3 (the last open cell in region 4), then H2 (the last open cell in region 2), then G8 (the last open cell in region 6), and the chain continues, and row 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
From there, every open cell in column E 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.
Following that, marking H2 would force F3 (the last open cell in region 4), then G8 (the last open cell in region 6), then A7 (the last open cell in region 8), and the chain continues, and then row 5 would be left with no open cell for its marker. So H2 can't be the marker there.
First, place a marker at F2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
Next, every remaining candidate in this region touches H4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, if B1 were the marker, it would force H3 (the last open cell in row 3), then G8 (the last open cell in region 6), then A7 (the last open cell in region 8), and the chain continues, and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
After that, that one can't be the marker: at H3 it would force G8 (the last open cell in region 6), then A7 (the last open cell in region 8), then D6 (the last open cell in region 7), and row 5 would be left with no open cell for its marker.
Now, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region. Placing here also clears its 1 touching neighbour.
From there, place a marker at A3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
Following that, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 1 touching neighbour.
First, place a marker at E5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region. Placing here also clears its 1 touching neighbour.
Next, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
Then, place a marker at C1. Region has exactly one open cell left.
Finally, place a marker at H6. Region has exactly one open cell left.

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