She succeeded in the attempt.

Literal

She [topic-は] that attempt [target-に] succeeded.

~に成功する ('succeed at/in') takes に to mark what was succeeded at — the field of success rather than the means. Distinct from English's 'succeed in,' Japanese keeps the target marker consistent: 仕事に成功する ('succeed at work'), 試みに成功する ('succeed at the attempt'). 試み ('attempt, endeavor, trial') is a relatively literary noun for 'a try' — slightly heavier than 試し or just やってみる.