Greetings, gentle patron!
If you are encountering difficulty making progress on my eighth ænigma, perhaps you'll find relief in one or both of the following pedagogical aids.
First, I have collected a small assortment of advisory notes, or ‘tips’ as one might say, which are enumerated a bit below on this page.
I trust that these resources will suffice to lift your mental ship off the shoals of perplexity and allow you happily to continue your journey down the river of clarity and decipherment, but if you find that they do not, I invite you to contact my associate, Pavel Curtis, directly for more individualized furtherance.
With my very best wishes for your imminent enlightenment,

As with so many ænigmas, it is ever so much easier to proceed when one has as much contextual information as possible. In this case, perhaps the most important information you can record is which squares you know cannot contain black squares. Each time that you can eliminate the possibility of a square being blackened, you make it that much easier to deduce which squares in the same row or column must be blackened. Pray do not hesitate to notate every such nonblack deduction (perhaps, as in the example, with a centered dot) immediately, as soon as you discover them.

Right at the beginning, and from time to time thereafter, you will encounter situations where an arrow points along a row or column that already contains the given number of black squares in the given direction. In such circumstances, you may instantly deduce that all of the remaining squares along that vector do not contain blackened squares and so notate them.

Symmetrically, you will occasionally discover that an arrow points along a row or column where there are only ‘just enough’ empty squares remaining to accommodate the requisite quantity of blackenings. For example, suppose that an arrow labelled “3” points along a direction containing only five empty squares, all together, and no previously blackened squares. Because the rules prohibit adjacent black squares, those five empty squares have only barely the capacity for the required three blackened ones, in the first, third, and fifth positions.

Every square that participates in the loop must be entered along that loop from one horizontal or vertical neighbor and then exited into another such neighbor. It follows therefore that an empty square with only one empty neighbor must not participate in the loop; that is, said square must be blackened (even if no arrow targets it).

A situation arises very commonly where you are considering whether or not a particular “candidate” empty square might be blackened. If one of its horizontal or vertical neighbors is an empty square that itself has exactly two empty neighbors, then you may conclude that the original candidate square cannot be blackened; otherwise, as noted in the previous paragraph, that neighbor of the candidate would also need to be blackened, a violation of the rules against adjacent black squares.
The simplest case of this situation occurs near the corners of the grid: if a corner square is empty, then neither of its neighbors can be blackened. However, the very same deduction applies much more generally, far from such an obvious corner position.

As always with my ænigmas, progress toward the solution here will come almost entirely in the form of small, incremental steps, often adding but a singleunit path segment, one blackened square, or a unitary knownnottobeblackened square to the grid. Do not endeavour to rush ahead, attempting to guess or otherwise ascertain the positions of several black squares or great lengths of path in one fell swoop. The whole of your solution will come as the sum of many steps; “patience” and “perseverence” must be your watchwords.
Wishing you the best of solving luck,

