A real important dream, like XXX, is worth every possible effort to guard

Firstly, use really, an adverb, instead of real, an adjective. I'm sure you know the difference, but basically, adverbs describe verbs, adjectives, or other verbs and an adjective describes a noun: really describes the adjective important, which in turn describes dream.

Of course, as important is quite a strong word, you could leave out the word really altogether.

There is nothing wrong with your phrase 'every possible effort to guard', it is just not idiomatic. You could use a more common turn of phrase, like 'is worth protecting at all costs'.

I would say:

An important dream, like one day being Prime Minister,
is worth protecting at all costs.

I'd say that protecting at all costs is a bit of a cliché. It's fine, but there's no harm in looking for a variant.

The problem with worth every possible effort to guard is that the reader is expecting the last word to be achieve. The sudden appearance of guard throws the reader, who then has to read the sentence again to understand the subtle difference.

An important dream, such as becoming Prime Minister, is well worth guarding. The guard is still at the end of the sentence, and the construction is well worth achieving is still possible, but the reader is less likely to be expecting it, and therefore is less likely to be thrown by encountering guarding instead.

An important dream, such as becoming Prime Minister, should be guarded with every sinew. Maybe the language here is a bit flowery, but it could be an option, depending on what effect you're going for.

(Note: My use of such as instead of like is probably just a personal preference.)