Readiness or mental preparedness — being mentally prepared for something (especially difficulties or danger).
手術の前に覚悟を決めた。
I made up my mind / prepared myself mentally before the surgery.
留学する覚悟はできているかと親に聞かれた。
My parents asked if I was ready (mentally) to study abroad.
悪天候でも出発する覚悟で準備を進めた。
We prepared to leave with the readiness to go even in bad weather.
Resolution or determination — a firm decision to accomplish or endure something.
彼は借金を返す覚悟でアルバイトを増やした。
He increased his part-time work with the determination to pay off his debts.
失敗してもやり抜く覚悟で挑戦した。
I challenged it with the resolve to see it through even if I failed.
合格する覚悟で毎日勉強している。
I'm studying every day with the determination to pass.
Resignation to one's fate — accepting an inevitable or unavoidable outcome.
手術の成功率が低いと聞いて、ある程度の覚悟はしている。
Hearing that the surgery's success rate is low, I have to some extent resigned myself to that.
覚悟を決めて別れを告げた。
I steeled myself and told them I had to part ways.
戦地に赴く兵士は死を覚悟していることが多い。
Soldiers going to the battlefield often accept the possibility of death.