I think it should be an idiom or sth like that. It has been used in the answer of this question: What is difficult when living in a different country?
I don't think it's really an idiom, it's just a literal phrase. Perhaps "papers" is a slightly obscure term for non-native speakers, though. "Papers" here is used as a catch-all for various documents, see definition 2.3 in Oxford dictionaries:
2.3 (papers) Documents attesting identity; credentials. ‘two men stopped us and asked us for our papers’
I think the phrase "obtaining the correct papers" is very literal and clear once you understand this usage of the word "papers". In the context of difficulties living in a different country, it refers to getting the various documentation that is required when living in that country. Exactly what that covers will vary depending on the country and various other factors. In general, it might include visas, residency permits, and legally-recognised proof of identity and address.