"One arrow two eagles"
To achieve two things despite taking only a single action
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运动真是一箭双雕，既能锻炼身体，又能调节精神 | Yùndòng zhēnshi yījiànshuāngdiāo, jì néng duànliàn shēntǐ, yòu néng tiáojié jīngshén
Exercising can really kill two birds with one stone. Not only can you train your body, but you can also regulate your [mood]
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我每天在家坚持画画，既动脑又动手，真是一箭双雕 | Wǒ měitiān zàijiā jiānchí huàhuà, jì dòngnǎo yòu dòngshǒu, zhēnshi yījiànshuāngdiāo
Every day I make a point to draw at home, which exercises both the mind and the hands. It really kills two birds with one stone
[Source]
To kill two birds with one stone
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《北史》(Běi Shǐ), a significant work in Chinese history that details events in the Northern Wei, Western Wei, Eastern Wei, Northern Zhou, Northern Qi, and Sui dynasties. It's known in English as "History of the Northern Dynasties" and was written by 李延寿（Lǐ Yán Shòu)
In the Northern Zhou Dynasty (北周, 557 - 581), there lived a man named 长孙晟 (Zhǎng Sūn Shèng). 长孙晟 had been a weak child, but his mother encouraged him to get stronger and to study, and he grew up to be an unparalleled archer in the imperial army.
Around this time period, there was an ethnic group called the 突厥 (Tū Jué). One day, the 突厥's khan came to the imperial court and asked to marry the emperor's daughter. The emperor agreed, and when it later came time to send the princess to the 突厥, the emperor asked 长孙晟 to escort her to her new home. 长孙晟 accepted, and soon he and the princess embarked their journey.
When they arrived, the khan was pleased to see 长孙晟. He knew that he was an exceptional warrior and archer, and after deciding that he wanted his services, he invited him to stay for a while. Unable to turn down the offer, 长孙晟 accepted.
For the year that 长孙晟 was with the 突厥, the khan often brought him along on hunts. Once, while they were out hunting, the khan saw two eagles fighting so ferociously over a piece of meat that it was hard to distinguish between them. He asked 长孙晟 whether he could shoot down the two birds, and the archer simply responded by urging his horse forward. He then nocked an arrow, aimed, and fired. The arrow pierced both of the birds at once, and they fell to the ground.