Hello,
It's hard to give detailed advice without more precise information about your work and your skills, but in this situation I would recommend working through the STAR (Situation - Task - Action - Result) framework.
Essentially, you begin your story with the “S”, situation, which is where you would provide context. In your case, this would be the specific context of your work. Try to keep it short, about 2-3 sentences, just keeping in mind what would be important for the interviewer to know to follow along. Then you talk about the “T”, task, which is what you had to do in the story. This can also be specific, and I would also advise to keep it short.
Now that you have set up the context, you can dive into the “A”, action, which is where you can talk about what you did in greater detail. In “R”, result, you talk about what exactly you achieved (which should be pretty unique - even if you are using a general skillset, the context in which you apply it is different).
In general, I wouldn't worry about having a generic skillset. Most of the qualities that fit interviews look for, such as leadership, initiative, teamwork, and so on, are very broad categories that can be met in a number of ways. So the goal isn't to show that you are the “best” at teamwork, just that you are very competent at it to a degree that would match the work requirements.