"She has not yet written a letter."

Translation: Вона ще не написала лист.

[smok_arman]

Using of noun "лист" in genitive case would be better here, so "Написати листа" must be the 1st option. "Написати лист" is acceptable also.
http://slovopedia.org.ua/34/53408/33113.html

[Udovytskyi]

In the negative expression only a genitive case is the semantico-stylistical correct translation

[stfods]

4 months, but still not accepted. Reported..

[Ktropin]

+1 should be 'листа'

[GeneM.]

Листа-I think I understand this from my Duolingo Russian lessons. So genitive is the best choice because we're talking about the absence of a letter (not yet written).

[Fokussnik]

You are right, it is not correct to use accusative with the negative statements, as well as genitive with the affirmative ones.

[va-diim]

In Polish, that's also the case. In Russian, objects in negation use accusative, unless directly negated.
Она не написала письмо. Нет письма.

[ferdinandkoenig]

I think this sentence is a little unfair for those who haven't studied this previously (or know Russian). How is learner supposed to know that negatives (can) take the genitive case? This is the first time it's introduced, without any warning.