。
She makes her living as a ballet dancer.
Literal
She [topic-は] ballet-dancer [as-として] livelihood [object-を] is-establishing.
生計を立てる ('to make a living, support oneself') is a fixed expression where 生計 ('livelihood, means of living') becomes the object of 立てる ('to establish, set up'). The progressive ~ている here marks the ongoing state of being self-supporting through this means — not a single act, but a sustained arrangement. ~として ('as, in the capacity of') is the standard particle for marking the role under which someone acts: バレエダンサーとして ('as a ballet dancer'), 学生として ('as a student'), 教師として ('as a teacher').