By all means; at any cost; expresses a strong determination to achieve something no matter what.
どうしても今度の試験に合格したい。
I absolutely want to pass this exam.
彼はどうしても夢を叶えようと努力している。
He is doing everything he can to make his dream come true.
Whether willing or not; expresses that something happens or is done regardless of one's preference.
仕事はどうしてもやらなくてはならないことがある。
There are things at work you have to do whether you like it or not.
彼女はどうしても参加させられた。
She was made to participate whether she wanted to or not.
On no account; by no means — used with negation to strongly deny that something can happen.
どうしても説明がつかないので、専門家に相談した。
I couldn't explain it no matter what, so I consulted an expert.
彼の行動はどうしても許せない。
I absolutely cannot forgive his behavior.
In the end; eventually — indicates that something happens after all or in the long run.
どうしても彼は最後に戻ってきた。
In the end, he came back after all.
いろいろ悩んだが、どうしても断ることにした。
After much thought, I ultimately decided to refuse.