yell at the top of one's lungs
上院に乗り込んでまで、中絶反対を訴えた人の記事です。乗り込むほどの行動力は正直羨ましいというか、凄いとは思いますが…
Screaming, bare-chested anti-abortionist removed from U.S. Capitol by cops
'The kingdom of God is at hand. I believe in the gospel,' Rives Grogan kept shouting as he was taken from the Senate gallery.
Anti-abortion protester, his shirt torn off, still yelling at top of his lungs as he's escorted from Senate gallery
A screaming, bare-chested protester was dragged out of the U.S. Capitol by police on Friday after he began shouting anti-abortion slogans from the Senate gallery.
『ジーニアス英和辞典』(第4版、大修館)ではshout [yell] at the top of one's lungsで「精一杯の声で叫ぶ」と定義されています。また、UsingEnglish.comには、At the top of my lungs "If you shout at the top of your lungs, you shout as loudly as you possibly can."と定義されています。yellだけでも大声で叫ぶ、大声をあげる、という意味がありますが、"as loudly as you possibly can"という説明からも読み取れるように、(出せる限りの)相当大きな声というニュアンスが読み取れます。
また、似たような表現に、to [at] the top of one's bent「力の限り」という使い方(ibid)もあるので、あわせて押さえておきたい表現です。(Astroriver)