  We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field
theory by uniting the non-perturbative methods of the conformal bootstrap and
supersymmetric localization, and utilizing special features of 3d ${\cal N} =
4$ theories such as mirror symmetry and a protected sector described by
topological quantum mechanics (TQM). Supersymmetric localization allows for the
exact determination of the conformal and flavor central charges, and the latter
can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE
data. We examine the implications of the $\mathbb{Z}_2$ mirror action for the
SCFT single- and mixed-branch crossing equations for the moment map operators,
and apply numerical bootstrap to obtain universal constraints on OPE data for
given flavor symmetry groups. A key ingredient in applying the bootstrap
analysis is the determination of the mixed-branch superconformal blocks. Among
other results, we show that the simplest known self-mirror theory with $SU(2)
\times SU(2)$ flavor symmetry saturates our bootstrap bounds, which allows us
to extract the non-BPS data and examine the self-mirror $\mathbb{Z}_2$ symmetry
thereof.
