If I am understanding you correctly, it seems like you are having trouble understanding where you can and cannot use incomplete sentences in writing.
In general, a complete English sentence contains a subject, a verb, and an object. There are some exceptions to this rule. For example, "Jim died" is an acceptable sentence, since the verb 'to die' doesn't modify an object.
Fragmented/incomplete sentences often leave out a subject, verb, and (optionally) an object that the verb affects.
"Leaving us alone." This sentence is incomplete because it doesn't have a subject. Who is leaving us alone?
To fix this, you can use a comma. "She closed the door, leaving us alone."
"A really good story." This is incomplete because it is only an object, and doesn't have a verb or a subject. To fix this, you can rewrite the sentence with a subject and a verb. "She told us a really good story."
The example you gave ("A promotion") is an incomplete sentence because it is only an object. You can use a colon to fix the sentence if you replace the object with a placeholder. In this sentence:
"He got what he worked for: a promotion."
The word 'what he worked for' is a placeholder for the object itself, which is 'a promotion'. You can think of the actual object as the surprise of the sentence, but you aren't going to reveal what the surprise is until after the colon.
You could also rewrite the sentence with a subject and an object, to say
"He got the promotion [that he worked for]."
In this way, the subject comes first ('He'), then the verb ('got'), then the object ('the promotion').
You can use incomplete sentences if they can be completed by the sentence before them. In the example you have given, "a promotion" is an object, but the subject and the verb are in the previous sentence ("He got what he worked for"). In the example sentence you are pointing to, "with difficulty" is a fragment, but can still be used because the reader understands the context from the sentence before it ("How did I escape?").
