"I am not afraid of anything."
Translation:Nie boję się niczego.
you can say "niczego nie rozumiem". you can always use "niczego" in genitive.
I think you can use both nic and niczego if the not negated verb requires accusative, but can only use niczego if the not negated verb requires genitive. (I can't find the rule anywhere, it always says both are correct if case is determined by a verb)
Also you use only "nic", if it is nominative, and if preposition requires accusative, and you use only niczego if preposition requires genitive.