Firstly, when answering this question always be truthful. Perhaps firms want to see certain skillsets / qualities in their candidates and your achievement does not cover those. But that does not mean it will count against you and therefore you must embellish or create new stories to reflect what they look for.
Instead, communicate that achievement clearly and concisely, highlight the value of it, your skillsets and qualities, and the importance of it to you. And if the achievemnet does not tick certain boxes that a consulting firm would appreciate, mention that although this did not involve me doing X, I did do that in another initiative for the firm on a separate occasion and I would be happy to detail what I did on that front and why I am great at it.
Firms typically value qualities such as being a self-starter, being proactive, having the ability to figure things out especailly with a great deal of uncertainty and a lack of direction/clarity, they will be looking for how well you applied problem-solving and analytical thinking, how you managed stakeholders, and what level of self-awareness / EQ you have. Consulting is a peoples business and therefore they will also be interested in how you manage relationships with others, in particular difficult characters, those that challenge you, those that give you feedback...
Tip of the day: for each firm, ask a consultant prior to the interview how their evaluations are performed (against what metrics / areas). And more likely than not, those areas will be sitting in the back of the interviewers mind when assessing your response (and in accordance to the position you are applying for)