For better or worse, there's no other way to get through this ordeal.
Literal
Good-or-bad, hardship [object-を] get-through [to-には] this [of-の] way [than-より] other does-not-exist.
良かれ悪しかれ ('for better or worse') is a classical-sounding set phrase — 良かれ/悪しかれ use the classical imperative-volitional forms of 良し/悪し. 乗り切る ('to ride out, overcome, get through') is a compound verb: 乗る + 切る ('cut through'). には after a verb's dictionary form marks purpose ('in order to').