When all-round records are tabulated in statistical articles, they invariably refer to feats of batting and bowling.
Here we look at feats of batting and fielding in the same match.
First, for wicket-keepers:
Century and 5 dismissals in an innings:

This did not occur in Tests until 1966. The best match performance would appear to be by de Villiers with a century and 11 dismissals in a match. Also consider Lindsay and Prior.
Watling appears here 3 times (twice in Wellington) along with Prior and Bairstow (twice each).
India has been on the receiving end twice: SAR Silva in 1985 and BJ Watling in 2014.
For non-keepers:
Century and 4 dismissals in an innings:

Bowling efforts have also been added where relevant.
We can see that Kallis’s feat in 2012 is clearly the best here, as he is the only double centurion here. Next would be Woolley.
Weekes did this against India in 1953, and was followed by fellow West Indian Viv Richards in 1989. Rahane did this for India against Sri Lanka in the course of the 3-0 sweep in Sri Lanka in 2017.
Next, we will look at career all-round performance for batting and fielding.
(To be continued)