  We report final measurements of direct $\mathit{CP}$--violating asymmetries
in charmless decays of neutral bottom hadrons to pairs of charged hadrons with
the upgraded Collider Detector at the Fermilab Tevatron. Using the complete
$\sqrt{s}=1.96$ TeV proton-antiproton collisions data set, corresponding to 9.3
fb$^{-1}$ of integrated luminosity, we measure $\mathcal{A}(\Lambda^0_b
\rightarrow p\pi^{-}) = +0.06 \pm 0.07\mathrm{(stat)} \pm 0.03\mathrm{(syst)}$
and $\mathcal{A}(\Lambda^0_b \rightarrow pK^{-}) = -0.10 \pm
0.08\mathrm{(stat)} \pm 0.04\mathrm{(syst)}$, compatible with no asymmetry. In
addition we measure the $\mathit{CP}$--violating asymmetries in $B^0_s
\rightarrow K^{-}\pi^{+}$ and $B^0 \rightarrow K^{+}\pi^{-}$ decays to be
$\mathcal{A}(B^0_s \rightarrow K^{-}\pi^{+}) = +0.22 \pm 0.07\mathrm{stat)} \pm
0.02\mathrm{(syst)}$ and $\mathcal{A}(B^0 \rightarrow K^{+}\pi^{-}) = -0.083\pm
0.013 \mathrm{(stat)} \pm 0.004\mathrm{(syst)}$, respectively, which are
significantly different from zero and consistent with current world averages.
