The "Over-Overkill" advancement can be granted as long as the player has the mace in their mainhand, without actually attacking with it. The following steps to reproduce it is how the challenge can be very easily achieved.

How to Reproduce

1. Have a parrot, a mace in your mainhand, and parrot poison in your offhand, usually a cookie
2. Feed the parrot.

Expectation

The parrot dies and the challenge isn't granted. And rightfully so.
Observation

Due to having the mace in your mainhand, the challenge is granted, despite not actually using it.