  In this work, we adapt the formalism of the dynamical vertex approximation
(D$\Gamma$A), a diagrammatic approach including many-body correlations beyond
the dynamical mean-field theory, to the case of attractive onsite interactions.
We start by exploiting the ladder approximation of the D$\Gamma$A scheme, in
order to derive the corresponding equations for the non-local self-energy and
vertex functions of the attractive Hubbard model. Second, we prove the validity
of our derivation by showing that the results obtained in the particle-hole
symmetric case fully preserve the exact mapping between the attractive and the
repulsive models. It will be shown, how this property can be related to the
structure of the ladders, which makes our derivation applicable for any
approximation scheme based on ladder diagrams. Finally, we apply our D$\Gamma$A
algorithm to the attractive Hubbard model in three dimensions, for different
fillings and interaction values. Specifically, we focus on the parameters
region in the proximity of the second-order transition to the superconducting
and charge-density wave phases, respectively, and calculate (i) their
phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of
the strong non-local correlations on the single-particle properties.
