。
She's working hard at her studies this semester.
Literal
She [topic-は] this-semester work-hard-and-then study is-doing.
頑張る (here in te-form がんばって) is one of the most distinctively Japanese verbs — 'to persist, to do one's best, to push through.' The te-form がんばって here chains adverbially with 勉強する: 'studying, with effort.' 頑張る is rooted in social culture: phrases like 頑張ってください ('please do your best') or 頑張ろう ('let's give it our all') saturate everyday encouragement. There's no clean English equivalent — 'try hard' is closer to 努力する, while 頑張る emphasizes endurance and commitment as much as raw effort.