Find in Panama

Banking in Panama is very hard if you are not a native of the city, but once you are able to jump through all the hoops your accounts will stay very private.  There are multiple kinds of banks available and it is important to realize some banks only do business with offshore accounts, some banks only do business with natives, and a few banks will work with both.  Also understand that banks in Panama are not federally regulated so there is no bank insurance when you open a bank account.  However, due to the amount of paperwork that is required to open an account, and the high level of privacy that banks offer in Panama, your money is pretty safe once it is deposited.
One of the reasons it is very hard to open a bank account in Panama is because of the high drug enforcement rates.  The government and people work very hard to keep the company free of drugs and drug dealers; therefore they are very suspicious of outsiders trying to take advantage of their private banking system.  To open an account one of the very first things you will need is proof of a substantial bank account balance in your home country and documentation showing where you obtained that money from.  Panama banking authorities want to know exactly how you earned your money to ensure you are not involved in unlawful activities in another country that you may be attempting to bring into their country.  Due to this fact, do not even consider trying to open an account with a large cash deposit, it will never be allowed.
In fact to open an account you are going to need proof of salary, a wire transfer from your home banking account, proof that you own a residence here, a cell and home phone number, and a multitude of references.  Basically the natives only will open their arms to those who are choosing to call Panama a home; there is no medium for people dropping by.  If you are planning on moving to Panama permanently, it is probably either best to hire a reputable lawyer from a large firm to represent you or wait until you obtain permanent residency in Panama.
On the bright side of things, due to the high privacy rules throughout Panama banks it is very unlikely any outside government or entity to which you have a current debt with will ever be able to access your bank account and seize your money.  If there is a very good cause for an outside government to be able to cease your money and the law you violated is also part of Panama enforced law, than eventually your money could be taken away, but it would take a long time for all the necessary paperwork to be filled out by each prospective government in order for a private bank to allow the account to be accessed.
In conclusion, banking in Panama is a possibility for non-Natives, but if one is not planning to make Panama there permanent place of residency than it is not worth it to even try to transfer funds.  The Panama bank system is built around a system that is very private, so if you can jump through all the requirements of the banks and the government it is possible to receive a bank account that is very secure and safe from outside creditor collections, but absolutely need to be able to prove the source of all your monetary assets and accounts.  Finally, if you do decide to open an account in Panama hiring a lawyer will keep you safe and aid you with the long drawn out process.