。
She tried various ways to lose weight.
Literal
[topic-は] become-thin [for-ための] various methods [object-を] tried.
やせる ('to become thin, lose weight') is a change-of-state verb — its bare form means the action of losing weight, while やせている describes the resulting state of being thin. やせるための ('for the purpose of losing weight') uses ための, the prenominal form of ために — placing a purpose clause before a noun ('various methods FOR X-ing'). 試す ('to try, test') is the standard verb for trying out methods or approaches; 食べてみる-style ~てみる would describe trying a single action.