At the most; at best — indicating the maximum or upper limit.
明日の会議にはせいぜい二十分しか参加できない。
I can only attend tomorrow's meeting for at most twenty minutes.
彼の貯金はせいぜい数万円だろう。
His savings are probably at most a few ten-thousand yen.
せいぜい頑張ってください（＝期待は控えめに）。
Do your best (with the implication that expectations are modest).
To the utmost; as much as one can — indicating doing something as much as possible.
試験まで残り時間は少ないが、せいぜい頑張ろう。
There isn't much time left until the exam, but let's do our best.
彼はせいぜいの努力を尽くしたが、結果は変わらなかった。
He did everything he could, but the result didn't change.