Translation:Of course she is serious.
I translated it as diligent (Mandarin is my mother tongue though I'm not totally fluent, taking this for fun)
In this sentence, is not appropriate to translate "diligent". Diligent means work hard, but in this sentence is not talking about attitude. If the question is asking about how he works, then this sentence suits.
I wanna show 2 different sentences, they're different.
她是認真的 She is serious, not kidding. She means it.
她很認真 She works hard, or study hard. Of course you can say diligent here. But, 勤勞 勤奮 are better translation.
If serious (认真) is an adjective, why is it connected to the person with the being verb 是? I thought you used a word like "hen" for that?