Yes, the second is the technically correct version. The first can be used conversationally, and it's a shortened version. Not optimal English, but used often enough to be acceptable nowadays.

I would go along with Andrew's version. I don't think it's to do with the education level of the speaker. In speech, people are likely to say 'how much time've you got left?' The 'have' is barely there when spoken naturally. It's not a nice clear 'have', native English speakers just don't talk that way. So first of all, it may be that you are missing this sound sometimes. However I do recognise what you have mentioned. Given what I said before, it is easy to see how it might become 'how much time you got left?' if people are speaking really quickly or just feeling a bit lazy. Like Andrew said, the latter is the correct form, which is used in writing.

For American English, I would say that Eva is correct. (How much time do you have left?) It's even more common to just say "How much time do you have?" ("left" is understood.)

You're right, it should be 'How much time have you got left?', but in rapid spoken language the 'have' is often barely audible. What we actually say is something like 'How much time'vyou got left?', or some people even drop the 'have' altogether. This is acceptable in informal spoken language. However, the only time you should write this is if, for example, you are writing a dialogue and you want to indicate that this conversation is informal. It is not standard written English.

It should be: ,,How much time have you got left?'' - less common, popular in British English or ,,How much time do you have left?'' - more popular, more common in American English. However, ,,How much time you got left?'' is incorrect and you can hear it only in spoken language and the people using it aren't very educated, I would say.