。
Her eyes had a pleading expression.
Literal
She [topic-は] eyes [at-に] pleading [possessive-の] expression [object-を] was-floating.
懇願の表情を浮かべていた — 懇願 (こんがん, 'earnest plea') is formal vocabulary. 表情を浮かべる ('to show an expression') uses 浮かべる in its 'to display/show' sense. Literary and descriptive.