One essential for a "good insulter" would be the ability to nose out some characteristic of the person being insulted, preferably one about which they feel a bit insecure, and use that as the basis for the insult, rather than just throwing out random off-the-shelf abuse. If an insult isn't in some way accurate, it's got no real force.

So, for exmple, to get back to the playground, there'd be no sense in calling someone who didn't wear glasses "old four-eyes".

Being a "good insulter" isn't something of which I'd pride myself.