The above sentence is an example sentence in an section of the Handbook that says 其 (기) can indicate the imperative when it "is placed directly before the verb and normally follows a noun or pronoun indicating the person or people being commanded." In other words, "Du's Handbook" is saying that 其 can be used simply as a marker or indicator of command sentences and, therefore, has no real translation except to tell you to think of the sentence as a command.爾其無忘乃父之志“Do not forget your father’s ideals!”
When I see something described as "a marker" or "indicator," I get suspicious. Do we really need a marker to tell us the above sentence is an imperative? I do not think so, so I want to suggest the following translation:
爾其無忘乃父之志"You (爾) promise (其) not (無) to forget (忘) your father’s wishes (乃父之志)."
My Korean dictionary says that one of the meanings of 其 (기) is "기약(期約)하다," which means "to pledge" or "to promise." Looking at the characters of 기약 (期約), I would guess that 其 (기) was sometimes used as an abbreviation of 期 (기), which also means "to promise." By translating the 其 (기) as "promise," the sentence still remains an imperative; the only real difference is that instead of calling 其 and "indicator" or "marker," it now has a real meaning.
By the way, 乃父 (내부) means "your father" and was how a father referred to himself when speaking to his children. The Korean equivalent would be "네 아비" or "이 아비." The 之 (지), of course, was the possessive marker changing "your father" into "your father's."