"I need to buy juice."
Translation:Мені треба купити сік.
This is a slightly complicated.
In Ukrainian, like in Russian, you can use genitive case for direct objects: «Мені треба купити соку» is perfectly OK.
However, unlike Russian, genitive case doesn’t always mean 'some'. Sometimes, it can mean a normal direct object. E.g. both «пишу́ листа́» and «Я пишу́ ли́ст» are possible as translations of 'I'm writing a letter', but «Я пишу́ листа́» doesn’t mean that you're writing 'some amount of a letter'. Both versions mean the same.
(Note that in Russian you can’t say «Я пишу́ письма́» with genitive, that wouldn’t make sense.)
So, in Ukrainian genitive direct object doesn’t always mean 'some'. The difference between «купи́ти сік» and «купи́ти со́ку» is not clear-cut, and it perhaps tells more about the dialectal background of the speaker, than about the meaning of the sentence.
If you want to express you’re buying a limited amount of juice, you could add something like «Я хо́чу купи́ти тро́шки со́ку» 'I want to buy a little juice'. That would work.