Learn Turkish: Rakip takımlar kıyasıya mücadele ettiler. - The opposing teams struggled fiercely.

The root is kıy-, meaning "to chop, act ruthlessly, or show no pity." Adding the converb of extreme limit -asıya literally translates to "to the point of having no pity." In modern Turkish, kıyasıya has become a very common fixed adverb meaning "fiercely," "ruthlessly," or "neck-and-neck," mostly used when talking about fighting or competing.

Is rakip acting as a noun or an adjective here?

It can be both, but here it acts as an adjective modifying takımlar. On its own, rakip means "opponent" or "rival" (a noun), but placed before another noun, it simply means "opposing" or "rivaling."

Since takımlar already has the plural -lAr suffix, why does the verb also take it (ettiler)? I thought verbs usually stay singular if the subject is explicitly plural.

You are remembering a good rule: if the plural subject is non-human (like animals or objects), the verb usually stays singular. However, for human subjects—or groups of people acting deliberately, like takımlar (teams)—adding the plural suffix to the verb is optional and very common. Here, it emphasizes their active, collective effort.

Why use mücadele ettiler here instead of kavga ettiler or savaştılar?