。
She hard-boiled the eggs.
Literal
She [topic-は] eggs [object-を] hard boiled.
固くゆでた — 固く (かたく, 'hard, firm') is the adverbial form of 固い, modifying ゆでた ('boiled'). ゆでる is written in hiragana here. 固ゆで is the standard term for 'hard-boiled.'
。
She hard-boiled the eggs.