Retina, 13 bytes

T`da-f`f-a9-0

This uses transliterate mode and its helpful feature that does reverse ranges, so f-a expands to fedcba. More thorough explanation coming soon.

Try the test suite online.

Retina, 13 10 bytes

T`w`G-A9-0

There are three parts to the code, separated by backticks (`): T specifies transliterate mode, which replaces each character in the second part with its corresponding character in the third part.

w is the same as traditional regex's \w, or _0-9A-Za-z, which is expanded to _0123456789ABCDEFGH....

The second part is expanded to GFEDCBA9876543210, thanks to Retina's nifty ability to expand in reverse order. Put these on top of each other, and we get:

_0123456789ABCDEFGH...
GFEDCBA987654321000...
 ^^^^^^^^^^^^^^^^

Note that the last character, 0, is repeated to fit the length of the longer string, but we only care about the hexadecimal characters, shown by carets.

Thanks to Martin Büttner for suggesting this approach.

Try the test suite online.

Retina, 13 bytes

T`da-f`f-a9-0

Try it online.

Retina, 13 bytes

T`da-f`f-a9-0

This uses transliterate mode and its helpful feature that does reverse ranges, so f-a expands to fedcba. More thorough explanation coming soon.

Try the test suite online.