I'm not sure if your client knows exactly what they are after, a responsive design is meant to fit at every screen width. So for it to be 'pixel perfect' you would need a design that works at 640px wide and one at 641px wide, as your images will be slightly bigger, some text might wrap differently. The idea is that content is fluid and fills that area that you show it.
There are a couple of options though when designing a responsive layout, one school of thought is to change the width of the browser on your design until the layout 'breaks' and then use that as the new width for your next design.
Another option would be to use a responsive framework like Bootstrap as the basis for your design. These frameworks still have fluid and full width components that will look different at every width, but also have some set breakpoints where things change.
So that doesn't really give you a hard answer, and is more like saying 'It can't really be exactly pixel perfect as the whole point is that it can change'.
But if you want some actual numbers, then depending on how the site is being built, you could opt for the dimensions that meet a framework like Bootstrap 4 - 544px, 768px, 992px, 1200px.
Bootstrap 4 Grid Options (alpha)