might and main

夏休みが終わってアンは勉強を再開するのにやる気満々です。
"I feel just like studying with might and main," she declared as she brought her books down from the attic.
"might and main" は初めて見る表現ですが、文脈からして全力でと言うような意味と推測できます。　辞書で確認します。
・Cambridge Idioms Dictionary: with all your effort and strength War is something we should be working might and main to avoid.
・McGraw-Hill Dictionary of American Idioms and Phrasal Verbs: Cliche great physical strength; great force. The huge warrior, with all his might and main, could not break his way through the castle gates. The incredible might and main of the sea crushed the ship against the cliff.
Dictionary.com: with all the vigor, force, or energy at one's command: They pulled with might and main.
"with all one's might" は見たことがありますが、似た表現に "with all one's might and main" もあるそうです。
私も "I will study English with all my might and main." と言えれば良いのですが、当面は英語より卓球、テニス、ランニングなどの体力増強の方にやる気満々なので、英語は頭の軽い体操程度で楽しみたい。