Learn Turkish: Bu göğsü kızıl tropikal kuş çok görkemli. - This crimson-breasted tropical bird is very magnificent.

This is a possessive compound adjective. To describe a specific feature of something, Turkish can take the body part/feature, add a 3rd person possessive suffix (here, -ü meaning "its"), and follow it with an adjective. It literally translates to "its-chest crimson." When put in front of kuş (bird), it acts as a single descriptive phrase: a "crimson-breasted" bird.

Why does the word for chest (göğüs) become göğsü instead of göğüsü here?

This is a classic case of vowel dropping (ünlü düşmesi). When certain two-syllable words—especially body parts like göğüs (chest), burun (nose), or omuz (shoulder)—take a suffix starting with a vowel, the vowel in their second syllable disappears. Therefore, göğüs + -ü (possessive) shortens to göğsü.

Could I use the "with/having" suffix and say kızıl göğüslü instead?

Yes, absolutely! Kızıl göğüslü (Red + chest + with) is the other standard way to form this kind of description. Both are grammatically correct and mean the exact same thing. However, the possessive compound göğsü kızıl often sounds slightly more literary, poetic, or formal, which pairs beautifully with a strong adjective like görkemli (magnificent).

Why is kızıl used here instead of the standard word for red, ?