Here is a hachure very interesting to explain techniques.
I give you some helps to use wave-logic four times, when you will have placed at least what you can of the 19, 21 and 23, and a part of the 5 below row L19, then completed.

Wave-logic R20-R21
There are seven cells still to blacken in R20, but only three in R21. So, there are at least four columns in which the 20th cell has to be blackened, without adding any black cell in R21. But, that's only possible in four columns:
- C5, if the 19 starts in R2 and ends in R20
- C11, because its 21th cell is already black
- C17 and C25, if a 1 starts and ends in L20.
We can thus blacken the 20th cell of each of this four columns and place a cross in their 21th cell if it is not already blackened.

Wave-logic R21-R22, R25-R24
In the same way, we can place the last 1 from C17 in L25, and the 21 and the 2 from C19 and C23 looking at transition R21-R22.

Wave-logic R23-R24
Finally, there are two cells still to blacken in R23, but only one in R24. So, there are at least one column in which the 23th has to be blackened, without adding any black cell in R24. That is possible in three columns:
- C13 and C15, if a 3 starts in R20 and ends in R23. But that's impossible, because that would induce one cell to blacken in R20 without overflowing onto R21, and the remaining clues numbers are too big.
- C21, if the 4 starts in R20 and ends in R23. That's possible, and as it's the last candidate, we can validate.
We can thus blacken R23C21 and place a cross in R24C21.

Hang in there...

Difficulty : *****

Tested, logical.
Wave-logic can be usefull.
Good blackenage.