Yes, it is correct. It is the third of the three forms of forming a question explained here:
Asking questions in French with "qui/que/quoi/quand/où/comment/pourquoi/combien" (French Question Words)

There are just two minor spelling errors:

- "Que" needs to be elided: Asking questions in French with "qui/que/quoi/quand/où/comment/pourquoi/combien" (French Question Words)
- A hyphen (trait d'union) is missing: The addition of the hyphen is explained when inverted questions are introduced: Inverted questions in the present tense (Le Présent) in French - regular forms (except il/elle/on forms)

So: "Qu'achètes-tu?"

The other options of forming this question are (see first link) with your variant being the most formal:

Qu'est-ce que tu achètes? (everyday usage)
Tu achètes quoi? (colloquial)

Tips:
- The kwiziq search enables you to find lessons on a topic of interest quite easily
- Computer based language tools have made immense progress and can be used for experimentation:
-- ChatGPT, Copilot (e.g. integrated in Microsoft Edge): For language learning these type of tools (large language models) are nothing less than a revolution. I put your question to Copilot and it did not point out the spelling errors until being poked. However, ChatGPT (GPT-4, paid version) nailed it on the spot.
-- Grammar checkers: These cannot be fully trusted but are quite good for checking simple texts. See Inverted questions in the present tense (Le Présent) in French - regular forms (except il/elle/on forms) It maybe sometimes quicker than using a ChatGPT type tool.
-- Translations tools like https://www.deepl.com/: Again, diminished value with the introduction of ChatGPT but lets you experiment more quickly. E.g. going back and forth between French and English.