Águila was a bad example. Let's try policía.
This is a really silly question, but I got distracted with El Águila Roja. Let's go back to something without another rule attached to it. I'm talking about nouns that end in A that can be either masculine or feminine, like policía, dentista, etc. I know the article changes, and I've always thought the adjective changes as well. A tall policeman is el policía alto, while a tall policewoman is la policía alta. Am I right so far? I learned these things back in the '70's, so there's a definite possibility some of those brain cells are no longer with us.
As a follow on question, if you have an animal, like a swallow, for example, that ends in A, am I wrong in thinking that a fat male swallow would be el golondrina gordo? Or are all fat swallows referred to as la golondrina gorda, regardless of sex?
2 Answers
Googling several articles on las golondrinas, I haven't found any consistent use of the articles, let alone adjectives. Several articles speak of los golondrinas machos while another uses la golondrina macho. Another used algunas golondrinas machos. I've yet to run across any use of an adjective modifying el/la golondrina macho.
Of course, la golondrina hembra is consistently feminine.

Applied to wild and some domesticated animals:
- Nouns where the two sexes of animals have different words to describe them: el toro/la vaca, el caballo/la yegua.
- Epicene nouns. The gender of the noun is fixed and sex is indicated by macho (male) or hembra (female). Examples: la jirafa macho, la jirafa hembra, el rinoceronte macho, el rinoceronte hembra.
So la golondrina macho is correct and el golondrina macho is incorrect.
Wait - I think I know the answer to my own follow on question. Animal nouns don't change gender, regardless of the gender of the animal. As a rancher, I know el caballo is the generic term for horse, while la yegua and el semental are mare and stallion. A chicken is el pollo, male or female, while a rooster is el gallo and a hen is la gallina. I think I've answered at least part of my own question. Articles and adjectives do not change, regardless of the sex of the animal.
I'm still curious about las golondrinas and the like, though, where I am unaware of other words for male and female.