Learn Finnish: Minä tarvitsen yhdet aurinkolasit matkaa varten. - I need one pair of sunglasses for the trip.

Aurinkolasit (sunglasses) is a plural-only word, meaning it is inherently plural even when referring to a single item, just like in English. When you count plural-only nouns or matched pairs in Finnish, the number must also be in its plural form. Therefore, 'one pair' is translated as yhdet.

Tarvita usually takes an object in the accusative or partitive case. Why does yhdet aurinkolasit look like it is in the nominative plural?

It is actually in the plural accusative! In Finnish, the plural accusative form of a noun is completely identical to the nominative plural, ending in -t. Because you need the entire pair of sunglasses, it takes the total object form, which for plurals looks just like the nominative plural.

Why is the word matka in the partitive case (matkaa) here?

It is driven by the postposition varten (for / for the purpose of). This postposition strictly requires the noun preceding it to be in the partitive case.

Could I say matkalle instead of matkaa varten?

Yes, saying Minä tarvitsen yhdet aurinkolasit matkalle (literally 'onto the trip') is also perfectly correct and very common. Using matkaa varten simply emphasizes the preparation aspect, meaning 'for the purpose of the trip.'