  In the last few years the derivative expansion of the Non-Perturbative
Renormalization Group has proven to be a very efficient tool for the precise
computation of critical quantities. In particular, recent progress in the
understanding of its convergence properties allowed for an estimate of the
error bars as well as the precise computation of many critical quantities. In
this work we extend previous studies to the computation of several universal
amplitude ratios for the critical regime of $O(N)$ models using the derivative
expansion of the Non-Perturbative Renormalization Group at order
$\mathcal{O}(\partial^4)$ for three dimensional systems.
