まずいよ。また遅刻だ!!はやくも遅刻魔の異名をとってしまう。

English Translation

Oh no! I’m late again!! I’m going to get the nickname ‘King of Late arrival’.

Incorrect word split.

(Current version) また遅刻だ!!は{{やくも}}遅刻魔の異名をとってしまう。

(Correct) また遅刻だ!! {{早くも}}遅刻魔の異名をとってしまう。

早くも is usually spelled in Kanji, not Hiragana.
早くも means “I haven’t been in this situation so long, but I have already XXX”. The root word 早い means “early”. In this lesson case, the Japanese sentence with 早くも suggests that “I’m a newbie here (at work or school), but I was late so many times. It’s too early for me to be called “the King of Late Arrival” by fellow students/colleagues.” I don’t find such a connotation in the English translation, so it should be also revised.