  We present the nonlinear growth of bound cosmological structures using the
spherical collapse approach in the shift-symmetric Galileon theories. In
particular, we focus on the class of models belonging to the Kinetic Gravity
Braiding by adopting a general parametrization of the action encoding a large
set of models by means of four free parameters: two defining the background
evolution and two affecting the perturbations. For the latter we identify their
specific signatures on the linearised critical density contrast, nonlinear
effective gravitational coupling and the virial overdensity and how they drive
their predictions away from $\Lambda$CDM. We then use the results of the
spherical collapse model to predict the evolution of the halo mass function. We
find that the shift-symmetric model predicts a larger number of objects
compared to $\Lambda$CDM for masses $M \gtrsim 10^{14} h^{-1} \mathrm{M}_\odot$
and such number increases for larger deviations from the standard model.
Therefore, the shift-symmetric model shows detectable signatures which can be
used to distinguish it from the standard scenario.
