。
She made sure to keep up with the latest trends.
Literal
She [topic-は] latest [genitive-の] trend [from-に] not-fall-behind [so-as-to-ように] was-doing.
The double-negative-ish structure ~に遅れないようにする packs three pieces: ~に遅れる ('fall behind X'), the negative ~ない ('not fall behind'), and ~ように+する ('make sure to'). The whole frame means 'to make a habit of not falling behind' — a way to express ongoing effort toward staying current. The past progressive ~していた locates this as an established habit she had been keeping up. 流行 ('fashion, trend') reads はやり for the everyday 'fashion,' or りゅうこう in the more formal Sino-Japanese reading.