How to solve this 8×8 logic puzzle

8×8 · severe · 21 steps

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This 8×8 board rates as severe (difficulty score 1217). Solving it from scratch takes 31 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

First, every remaining candidate in this region touches B8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Next, marking A1 would force B7 (the last open cell in region 8), then E6 (the last open cell in region 6), then F8 (the last open cell in region 7), and the chain continues, and then column G would be left with no open cell for its marker. So A1 can't be the marker there.
Then, if B1 were the marker, it would force D3 (the last open cell in row 3), then C5 (the last open cell in region 3), then H4 (the last open cell in row 4), and column G would end up with no open cell for its marker, which can't happen. So it can't go there.
After that, marking D1 would force E5 (the last open cell in region 4), then H4 (the last open cell in region 5), and then column G would be left with no open cell for its marker. So D1 can't be the marker there.
Now, marking G1 would force A2 (the last open cell in row 2), then B7 (the last open cell in region 8), and then column C 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 A5 (the last open cell in region 6), then C4 (the last open cell in region 3), and row 3 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, if F2 were the marker, it would force C1 (the last open cell in region 1), then G6 (the last open cell in column G), and column H would end up with no open cell for its marker, which can't happen. So it can't go there.
Next, if A3 were the marker, it would force B7 (the last open cell in region 8), then E6 (the last open cell in region 6), then D4 (the last open cell in region 4), and the chain continues, and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
Then, marking H2 would force D3 (the last open cell in row 3), then A5 (the last open cell in row 5), and then row 4 would be left with no open cell for its marker. So H2 can't be the marker there.
After that, place a marker at A2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
Now, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region. Placing here also clears its 2 touching neighbours.
From there, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 2 touching neighbours.
Following that, place a marker at C1. Column 3 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
First, 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.
Next, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region.
Then, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
After that, 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.
Now, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region. Placing here also clears its 1 touching neighbour.
From there, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
Finally, place a marker at D4. Region has exactly one open cell left.

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