to pass the peak (of difficulty); to get through the worst part; to be over the worst (e.g., an illness or crisis)
入院していた祖母の容体はようやく峠を越えたという。
They say my hospitalized grandmother has finally passed the worst.
夏の売上不振は一時的で、会社は峠を越えたと報告された。
The summer sales slump was temporary; the company reported that it had passed the worst.
長引いた工事のトラブルも、今月で峠を越える見込みだ。
The prolonged construction troubles are expected to get past the worst this month.
to cross a mountain pass; to go over a pass (literal)
ハイキングで峠を越えて向こう側の谷に下りた。
On the hike we crossed the pass and descended into the valley on the other side.
雪のため車で峠を越えるのは危険だ。
It's dangerous to drive over the pass because of the snow.