The eligibility requirements for a Citizenship by investment visa are different from country to country. But in general you will have to prove the following:
MONEY: You would need to prove that you own the money intended for investment and that it was legally acquired.
CRIMINAL RECORD: Your criminal records are to be checked. The background check is to show you have no history of criminal records.
SUSTENANCE: Proof that you can sustain yourself and family members for the period of time you intend to live there.