。
She came in first in the eating contest.
Literal
She [topic-は] big-eating contest [in-で] number-one became.
大食い ('big eating, gluttony') is the noun form of the verb 大食う ('eat large amounts'); 大食い競争 ('big-eating contest') is the standard term for an eating competition — a recurring spectacle on Japanese variety TV (especially with celebrity 大食いタレント like 木下ゆうか or 小林尊). 一番になる ('become number one') is the standard 'come first / win' construction, with 一番 ('number one') in the role of the resulting state.