  We explore the potential of precision cosmological data to study non-minimal
dark sectors by updating the cosmological constraint on the mirror twin Higgs
model (MTH). The MTH model addresses the Higgs little hierarchy problem by
introducing dark sector particles. In this work, we perform a Bayesian global
analysis that includes the latest cosmic shear measurement from the DES
three-year survey and the Planck CMB and BAO data. In the early Universe, the
mirror baryon and mirror radiation behave as dark matter and dark radiation,
and their presence modifies the Universe's expansion history. Additionally, the
scattering between mirror baryon and photon generates the dark acoustic
oscillation process, suppressing the matter power spectrum from the cosmic
shear measurement. We demonstrate how current data constrain these corrections
to the $\Lambda$CDM cosmology and find that for a viable solution to the little
hierarchy problem, the proportion of MTH dark matter cannot exceed about $30\%$
of the total dark matter density, unless the temperature of twin photon is less
than $30\%$ of that of the standard model photon. While the MTH model is
presently not a superior solution to the observed $H_0$ tension compared to the
$\Lambda$CDM+$\Delta N_{\rm eff}$ model, we demonstrate that it has the
potential to alleviate both the $H_0$ and $S_8$ tensions, especially if the
$S_8$ tension persists in the future and approaches the result reported by the
Planck SZ (2013) analysis. In this case, the MTH model can relax the tensions
while satisfying the DES power spectrum constraint up to $k \lesssim 10~h\rm
{Mpc}^{-1}$. If the MTH model is indeed accountable for the $S_8$ and $H_0$
tensions, we show that the future China Space Station Telescope (CSST) can
determine the twin baryon abundance with a $10\%$ level precision.
