"She is making every effort not to cry."
Translation:היא עושָה את כל המאמצים לא לבכות.
Well, yes, this is one way to transform the phrase into a sentence. As for my question, formal usage tends to add שֶׁ־ּ to the לֹא, when negating infinitives (Glinert §29.8), f.e. הֶעֱדַ֫פְתִּי שֶׁלֹּא לְהִתְעָרֵב I preferred not to interfere. The same holds true for adverbials of more than one word: שֶׁלֹּא כְּמוֹ יְרִיבַי, הִתְחַ֫לְתִּי… unlike my opponents, I began… Interestingly he writes that he sees no obvious connection to the usual שֶׁ־ּ meaning that.
Very interesting and useful comment, thank you Ingeborg. But "he sees no obvious connection to the usual שֶׁ־ּ meaning that. " -- so what other kind of שֶׁ־ּ is there? I've never seen or heard שֶׁ־ּ, so far as I know, with any meaning other than "that" either as a subordinating conjunction (e.g. I know that it's true) or as a relative pronoun; originally a contraction of אשר , I believe.
Well, there is, as you said no other שֶׁ־ּ in the language, so I suppose he wants to express that this relative particle is used outside its normal grammatical range. But indeed me being puzzled by his remark was the reason I mentioned it. Contrary to your assumption I do not think שֶׁ־ּ to be a contraction of אֲשֶׁר. Ugaritic uses aṯr as where, that which which is related with Aramaic אֲתָר place (Hebrew site), so that אֲשֶׁר was originally something like the place where and was then generalised. On the other hand there is the Assyrian determinative pronoun ša, which can introduce subordinate clauses, which is also visible in Phoenician שׁא. So the origin of the two Shins seem to be originally different phonemes and some write, שֶׁ־ּ was a dialect word of the Northern kingdom of Samaria.