The key is to write factually without emotion and to be clear. To take two examples from your text: "she has repeatedly forgotten a crucial retaining clip on a certain sub-assembly so that under testing pressure, the person doing the testing has nearly been badly injured by a part getting shot out because it had no retaining clip on). We have soft hose that we cut to custom lengths; I've shown her several times, as have other people, how to cut it straight, instead of cutting it crooked, then trying to straighten the crooked cut by "trimming" the hose. Yet I'll see her having cut several pieces of hose crookedly and she is surrounded by a mountain of hose trimmings. That's quite a bit of wastage. We keep telling her if she is cutting the hose properly, there is no need for trimming; she keeps insisting it's the end result that matters and her cut pieces are fine. We keep pointing out how much she wastes a)by trimming and b) because the pieces she has trimmed bits off of are now too short"
I'd start with a summary and then move to examples:
X consistently shows a lack of attention to detail and despite repeated training is unable to master the basic tasks required for the job. Her continued lack of improvement suggests to me that additional training is not likely to improve the situation. Following are specific examples:
X has been trained to assemble Y by Z on MM,DD,YYYY, yet she repeatedly (X times) has forgotten a crucial retaining clip when assembling this on her own. This represents a known danger to other employees and during routine testing prior to shipping a part has shot out and come close to injuring the person doing the testing on Y occasions (documented in the following safety incident reports). On each occasion X was informed of her error and retrained on how to properly assemble Y.
X has been trained to cut soft hoses by Z on MM,DD,YYYY and has not mastered this skill. Her cuts are consistently off and require additional trimming thus wasting product, requiring additional time, and resulting in an end product that is too short. She has been informed of this problem multiple time (X times) and retrained on each occasion, yet continues to be unable to master this task.
Ideally you will also be able to add specific dates for her training.