Using the same island used in the Feather Mouth achievement.
In Nature Form, you can single-tap your right-mouse-button to launch and create a small sprout of flowers. If you hold the right-mouse-button and charge the shot before releasing, you will sprout a large green stalk.
Aim one of these charged shots at/under a monkey - it'll go flying off and you'll get the achievement.
Steam Achievement: Monkey Flinger - Fling a Monkey.
Disclaimer: I do not own, or claim to own, any part of the displayed content - the art, music, etc...was all created by, and is owned/copyrighted by, the independent developers over at Bit Blot - the creators of Aquaria. I have no affiliation/association, or claim to have any affiliation/association with BitBlot. I am nothing more than a customer who purchased Aquaria on Steam, played it, loved it, enjoyed it, and wanted to post a play-though for Aquaria.