A dancer's grace is born from strenuous practice, sweat, and suffering.

Literal

Dancer [possessive-の] grace [topic-は] strenuous [attributive-な] practice, sweat [and-と] suffering from is-born-[explanatory-のです].

懸命 is a na-adjective 'strenuous / desperate,' sharing its core 懸命 with the four-character 一生懸命 — both rooted in the medieval samurai sense of 'risking one's life.' 生まれる here is metaphorical: 'born from X' = 'comes from / arises from X.' The から marks the source of origin. A poetic aphorism about the hidden cost of beauty.