  The precise estimation of the statistical errors and accurate removal of the
systematical errors are the two major challenges for the stage IV cosmic shear
surveys. We explore their impact for the China Space-Station Telescope (CSST)
with survey area $\sim17,500\deg^2$ up to redshift $\sim4$. We consider
statistical error contributed from Gaussian covariance, connected non-Gaussian
covariance and super-sample covariance. We find the non-Gaussian covariances,
which is dominated by the super-sample covariance, can largely reduce the
signal-to-noise of the two-point statistics for CSST, leading to a $\sim1/3$
loss in the figure-of-merit for the matter clustering properties
($\sigma_8-\Omega_m$ plane) and $1/6$ in the dark energy equation-of-state
($w_0-w_a$ plane). We further put requirements of systematics-mitigation on:
intrinsic alignment of galaxies, baryonic feedback, shear multiplicative bias,
and bias in the redshift distribution, for an unbiased cosmology. The $10^{-2}$
to $10^{-3}$ level requirements emphasize strong needs in related studies, to
support future model selections and the associated priors for the nuisance
parameters.
