Sorry to post in an almost 1 year old thread, but I just checking the old ones and see that this here may still be a valid question which never got answered.
From where you made the post it seems you are looking for a Cyprus bank account, so the answer is, there are no special requirements. You just need a valid governement issued photo ID and a utility bill not older than 3 months and finally in certain cases a reference letter!
If it is a company, you will need all corporate documents i.e. Memorandum & Articles with Apostille.