Takota Splendor was already used to sleeping in trees. However, she knew she could never get used to the sound of drilling in the morning. A woodpecker was just above her head, tediously boring into the tree. Takota’s light-brown eyes squinted open and she peered up at the redheaded bird, with its sharp-edged bill. It paused and stared down at her, as if to say, “I just so happen to do this every morning and if you’re going to start complaining now you had best find another tree to sleep in, not that I would recommend humans sleeping in trees.”
Takota smirked in response to the bird’s stare. The woodpecker turned and continued drilling, paying her no mind. She sighed and finally leaned up on the broad branch. She swung down out of the tree just as a cardinal, with its rich red feathers,

A few little quibbles:

Try to re-write the second sentence do it doesn't begin with "However" - it just feels a little week to me.

The world 'already' implies she hasn't been doing it long and this needs to be explained in the first sentance or one sentance later.

'she knew' ... if she didn't know, we wouldn't see it in print unless the PoV is broken. No need to say 'she knew'.

"A woodpecker was just above her head, tediously boring into the tree." - rewrite this to not use "Was"

Why do we need to know her eye color? If its not relevant to the story and this is not a romance novel, we don't really need to know.

The woodpeckers gaze seems wordy.

"...to the birds stare." We get what she is responding to. No need to it to be stated explicitly.

would do better IMJ as

However, she knew she could never get used to the sound of woodpeckers drilling in the morning. A woodpecker ...

That's so I don't have time to get images of pneumatic drills or power tools in my mind!

But I kind of like this beginning. BTW I liked the woodpecker's 'words'.

I'll put my two cents in on the woodpecker's speech: for my taste it was much too long. A simple look could not have conveyed such complex ideas. If Takota has special abilities to communicate with animals, better to italicize them and call a speech a speech. Although a shorter version of the woodpecker's "as if to say" would be well-placed.

I also agree with pantros about not needing to know the color of Takota's eyes. It is especially distracting given the fact that you're about to describe a "redheaded" bird. Since redhead is commonly a way to describe a person's hair color, it feels for a moment as though the description of Takota is continuing, and makes the brown eye description jump out at the reader more than it generally would.

A few other nits:

I don't think the adverb "already" is necessary in the first sentence.

On a similar theme, the adverb "finally" doesn't add anything to the penultimate sentence.

Once again, the title, writing style, character, and setting had a nice internal harmony- very fresh and "woodsy" (now I sound like I'm talking about furniture polish sorry).

Good luck with your revisions!