。
She has been through many painful experiences.
Literal
She [topic-は] many [genitive-の] painful feelings [object-を] has-experienced-up-to-now.
辛い思い ('painful feelings / hard experience') uses 思い (the noun form of 思う) in the sense of 'subjective experience / feeling' rather than 'thought.' The collocation ~思いをする 'have a (X) experience' is productive — 嫌な思いをする ('have an unpleasant experience'), 悲しい思いをする ('feel sad'). Here it pairs with 経験する ('experience') for a slightly redundant but standard phrasing. ~てきた marks accumulating events up to the present.