T tells you that “FALSE” is in the second row. It’s a five-letter word, so it takes up the whole row, either forwards or backwards. Either way, L goes in Cell 8.
L tells you that S cannot be adjacent to T. So now you know that “FALSE” is forwards, from Cell 6 to Cell 10.
F tells you for sure that 11-16-21 is either D-U-G or G-U-D. L tells you that G cannot go in cell 11, so it must be D-U-G.
T told you that you were looking for “SHOW.” There’s no longer anywhere to form a four-letter word starting with S, except straight down. So 14-19-24 are H-O-W.
O tells you that Cells 5 and 15 are X and Q or vice versa. A told you that you were looking for “BIN” in the top row. Now you know it must be in Cells 2-3-4. But B cannot go in Cell 2, according to L, or it would be adjacent to A, so Cells 2-3-4 are N-I-B.
I tells you that Cell 13 must be C.
C tells you that Cell 12 must be R.
O told you that Cell 15 is either X or Q. R tells you that it cannot be X, so Cell 15 is Q.
So, according to O, Cell 5 is X.
F tells you that V is the missing letter. You know from G that Y is either in Cell 17 or 18. This means, according to L, that Z cannot be in any of Cells 17, 18, 22, or 23. And X tells you that Z is not in Cell 20, so Z is in Cell 25.
The remaining letters are J, K, M, P, and Y. You know that M, P, and Y are in the 2×2 square of Cells 17, 18, 22, 23. Q tells you that the remaining letter in that 2×2 square is K. So J must go in Cell 20.
G told you that C is adjacent to Y. J tells you that Y is not adjacent to U. Therefore Y is in Cell 18.
If P is adjacent to Cell 22, then P is not in Cell 22. So, according to Cell 13, P is in Cell 17.
No row is currently in alphabetical order. The remaining letters are K and M. So according to P, K is in Cell 22 and M is in Cell 23.