Start with the English:
> Not (everyone who kills a sith succumbs to the dark side)
Give the implicit people names:
> Not (everyone, $a$, who kills a sith, $b$, succumbs to the dark side)
Not is a '$\
eg$':
> $\
eg($ for everyone$, a,$ who (kills a sith $b$) implies $a$ succumbs to the dark side)
Saying (kills a sith $b$) can be translated as $\exists b(b$ is a sith and $a$ kills $b)$
> $\
eg($ for everyone, $a$, $\exists b(b$ is a sith and $a$ kills $b)$ implies $a$ succumbs to the dark side)
quantify over $a$ to account for 'everyone':
> $\
eg\forall a( \exists b(b$ is a sith and $a$ kills $ b)$ implies $a$ succumbs to the dark side)
finish:
> $\
eg\forall a(\exists b(Sb\wedge Kab)\rightarrow Da)$