The best place to pick this up is the little "island" to your left, your first time crossing The Veil - to the right of the fast-travel sea turtle and the Save Crystal.
Get into Beast Form, hop up onto the island, use the middle-mouse button (or other look-around key you may have bound) to scan the sky above for a passing parrot. Once you spot one, track its movement carefully and aim a lunge at it. Nomnom parrot.
Steam Achievement: Feather Mouth - Devour a Parrot.
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.