It is an elliptic form of a dream that has come true; you can see it as an example of a perfect passive participle (i.e. past participle). English-test.net sports a question similar to yours, and one of the answerers posted:
...not only is "dream come true" a set expression, but it is also perfectly correct from the grammatical point of view, because, as I'm sure you know, the verb "come" is irregular (come - came,come) whose "infinitive" form is identical to "past participle". Here the expression "to come true" (which means "to materialize, become a reality, become fulfilled" is used with the verb in the "past participle" form by analogy with "girls gone wild" or "teacher turned gangster". In other words, nothing to be surprised or puzzled by, because in this case everything makes perfect sense, even though in language it does not have to be this way.
I think "come" is a past participle acting acting as an adjective here.
The dream has come true, it is a dream come true.
...[Member 1]'s explanation is the right one. In this expression, "come" is a past participle (with the verb "come" here meaning "become"), and the participial phrase "come true" is used as an adjective.
Here are other similar participial phrases used as adjectives:
She was an actress adored by her fans, but thought cold by those who knew her well.
The billboard was seen daily by thousands of people.
So your first explanation is half correct in that that has come true can be consolidated to the participial phrase come true. However, your third option is the closest, as evidenced by the explanations I quoted.