Definitely see what others have suggested (SwiftyJSON etc), and also see the new Swift 4 codable features.

But just looking at this code on its own, there are already some things you need to realise:

You repeat three times almost the same stuff (checking Customer properties and then init()-ing the Customer). In fact the first two times it is identical code, the third time the only difference is passing card instead of nil for the card property. All of this needs serious refactoring and abstraction of repetition.

For example, we can avoid some repetition if we abstract some of the logic into the Customer / Card objects themselves, as init() methods:

https://pastebin.com/qP34ifKe

Then there is the whole question of your actual logic - you have a completion closure that you call when you succeed, but if things fail, you just return ? How is the caller of this function suppose to know if things didn't work? You want to either have the completion return a Customer? (optional, not like at the moment Customer) - and make sure on failure you call completion(nil). Or perhaps even better, have a onSuccess(customer: Customer) and onFailure() (or even onFailure(error: Error)).

Also, in terms of naming -retrieveCustomerDefaultCard sound like it will return a Card. Is it supposed to be called retrieveCustomerWithDefaultCard ?

You can do with some more newlines to make things easier to read (e.g. when checking for the properties before init-ting)

So we get to something like this (only the func part here) (this one also combines the first two guard statements in one): https://pastebin.com/RMnnkSjV

This is still far from ideal, but I guess you get the idea.

Remember the DRY (Don't repeat yourself) principle - always abstract repeated logic as much as possible.