Use the letter for information that benefits from context. That usually includes why the firm or office makes sense for you, one or two experiences that demonstrate relevant consulting skills, and a clear explanation of why you are making this career move.
You do not need to cover every achievement. Pick evidence that supports the story you want the recruiter to understand. If a bullet already speaks clearly for itself on the resume, repeating it word for word in the letter wastes space.
Specificity is what makes the letter useful. Mentioning a relevant office connection, practice interest, or experience can make the motivation feel real instead of generic.
Think of the cover letter as the narrative around the resume, not a second version of the resume.