  We study the quantum phase transitions of a disordered two-dimensional
quantum anomalous Hall insulator with $s$-wave superconducting proximity, which
are governed by the percolation theory of chiral Majorana fermions. Based on
symmetry arguments and a renormalization group analysis, we show there are
generically two phase transitions from Bogoliubov-de Gennes Chern number
$\mathcal{N}=0$ to $\mathcal{N}=1$ ($p+ip$ chiral topological superconductor)
and then to $\mathcal{N}=2$, in agreement with the conclusion from the band
theory without disorders. Further, we discuss the critical scaling behavior of
the $e^2/2h$ conductance half plateau induced by $\mathcal{N}=1$ chiral
topological superconductor recently observed in the experiment. In particular,
we compare the critical behavior of the half plateau induced by topological
superconductor with that predicted recently by alternative explanations of the
half plateau, and show that they can be distinguished in experiments.
