The sadness was so piercingly intense that she couldn't even cry.

Literal

She [topic-は] sadness [subject-が] too [poignant-痛切で] tears [also-も] didn't-come.

あまりにも痛切で — あまりにも intensifies to 'far too.' 痛切 ('poignant/piercing') is a literary Sino-Japanese compound for emotional pain.