Has any moon achieved "retrograde equatorial orbit"?
This is directly related to another question: Why are asteroids with zero orbital inclination rare?
If captured, irregular moons are randomly oriented in space then there is very little chance of them having either inclination angles near zero or near $180^\circ$. This is because, if they are uniformly distributed in space, the fraction of orbits within a given inclination range $i_1 &lt; i &lt; i_2$ is given by
$$ f = \frac{\int^{i_2}_{i_1} \sin i\ di}{\int_{0}^{180^\circ} \sin i\ di}$$
$$f = \frac{1}{2}\left(\cos i_1 - \cos i_2\right)$$
Thus for $i_1 =177^\circ$ and $i_2=180^\circ$, $f= 0.00068$ (i.e. about 0.07%).
Given that there are only $\sim 100$ irregular satellites, it is not that surprising that none are found with $i&gt;177^\circ$.
Note there are physical reasons why the regular satellites have low inclinations - they are not uniformly distributed and therefore they can have very low inclinations.