Why is 是…的 used?
If I'm not wrong the pattern “是 + adjective + 的“ is used to emphasize the adjective. In this case it would mean: "She is NOT SERIOUS".
认 (recognize) + 真 (real/true/genuine) = 认真 (serious)
Would it be grammatically correct if you omit 是 and / or 的?
Why so serious?