When a rhyming text is translated into another language, how is all the rhyming maintained?

1. It isn't.  The meaning is faithfully translated, which often means most of the rhymes are lost (but sometimes, by chance, some of them remain).  Sometimes though the nature of the language makes rhyming fairly easy with certain parts of speech.  However, that's rarely true when translated into English. 

2. The words are changed to force the rhyme. Often there is effort to preserve the meaning as much as possible, while using different structures or word order. 

I have seen many English songs translated into French, both ways.  When #2 is used, the literal meanings aren't identical for every line, but often the main message remains true. 

one example:  One translation of the Greatest Showman's, This Is Me, translates the line "For we are glorious" as "a world to conquer" to rhyme with the previous line.

Note that #1 is often unnatural in the target language.  "This is Me", for example, although can be translated literally, for right, wrong, or indifferent, is translated as "I am me". 

It isn't.  Translating poetry is far more difficult that translating prose.  Just look at the books of the Bible - a lot of them are poetry, or acrostic, and things like that, but, we just cannot see it when we read it in English, other than the flowery language of some passages.

It can be possible to translate the essence as to what was said into poetry, but, this is super difficult.