。
She tried not to show her sadness at the party.
Literal
She [topic-は] party [at-で] own [genitive-の] sadness [object-を] not-show [in such a way as to-ように] did.
~ないようにする is the standard pattern for 'try not to / make sure not to / take care not to do X' — built from the negative form of a verb plus ようにする ('make it so that'). The contrast with 見せなかった ('did not show') is important: the ~ないようにする framing emphasises conscious effort and self-control, while the bare negative would simply state the absence of the action. 自分の悲しみ ('one's own sadness') is heavier and more abstract than the more conversational 悲しい気持ち; this register choice gives the sentence a slightly literary, introspective tone.