First of all, "it's" is a contraction of "it" and "is." You want the possessive form "its" with no apostrophe. Also, a more common way of expressing this is to refer to a butterfly "coming out of its cocoon" or more poetically "emerging from its cocoon." It's used as a metaphor for a new beginning: Her new look gave her so much confidence that she seemed like a butterfly emerging from its cocoon.

In any sentence, you can replace the word "butterfly" with "butterfly crawling out of its chrysalis". So, if you have a sentence using "butterfly", you also have a sentence using "butterfly crawling out of its chrysalis". The clause "crawling out of its chrysalis" behaves as an adjective modifying "butterfly". Example: "I see a butterfly resting on a rose" becomes "I see a butterfly crawling out of its chrysalis on a rose".

This sounds like a caption to a photograph. It is not a complete sentence. It is very common to use a brief description, which is not a complete sentence, as titles or captions in order to save words. For example, you may see a headline on a newspaper that says: Tornado Damage in Alabama. That is not a complete sentence but it conveys the gist of what the article will be about.

Butterflies crawling out of their chrysalis are a wonder of nature. It works with the plural too.