  We construct the general solution of a class of Fuchsian systems of rank $N$
as well as the associated isomonodromic tau functions in terms of
semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$.
The simplest example is given by the tau function of the Fuji-Suzuki-Tsuda
system, expressed as a Fourier transform of the 4-point conformal block with
respect to intermediate weight. Along the way, we generalize the result of
Bowcock and Watts on the minimal set of matrix elements of vertex operators of
the $W_N$-algebra for generic central charge and prove several properties of
semi-degenerate vertex operators and conformal blocks for $c=N-1$.
