I don't know if there's still a use for such a skill, but if you care, I learned it as a set of 8 pairs: first, 0 and F are easy, right? 9 and 6 are 1001 and 0110, and a 9 looks like an upside-down 6 so hopefully you can remember that pair.
That leaves 12 digits, and they come in mirror-image pairs: 1/8, 2/4, 3/C, 5/A, 7/E, B/D. You know which hex digit is larger, and the larger binary is heavier on the left side, e.g. D is 1101 and B is 1011.