PPC agent's goal #1: Restore continuum to original status.
PPC agent's goal #2: Get back at the badfic for the insanity suffered.
Luckily, the two goals fit together nicely because irony, like any law of narrative comedy, tends to play itself out very often in PPC missions; and one very classic kind of irony is when a bad guy is killed in an ironic fashion--in this case, killed by the continuum he was trying to distort. We're talking Sues here, for the most part (some other phenomena may also be subject to this, such as mini-Sues, author-wraiths, badfic authors at OFUs, uncanonical locations, and misbehaving PPC agents).
It's generally thought that the more canonical and "fitting" the punishment is, the better the canon can recover from the Sue's damage. For example, a witch!Sue in a Harry Potter fic often ends up burned with the Incendio charm--doubly ironic, because she's being targeted by Potterverse magic (a canonical method of demise--highly preferred) and is being "burned as a witch"!
But that's not the only thing that has to be taken into account. Not only does an execution have to be fittingly ironic; it also can't get too old. The less cliched an execution strategy is, the better it seems to work. Witch-burning, in this case, has unfortunately been used quite a few times. Other examples include feeding Sues to the Balrog or the Watcher in the Water. The more unusual, the less often an execution method can be repeated and retain its efficacy. The businesslike executions favored by assassins who prefer to just "get the job done" without any extra frills (bullets, arrows, knives, etc.) don't seem to suffer at all from the problem of being cliched, no matter how often they are used.
I should, however, note that it's important not to be *too* elaborate with executions. Canonical and ironic, or else businesslike and quick, tend to be the best ways to go about the execution. Torture is absolutely forbidden, though it has happened in the past, because it's generally a bad idea to generate any kind of sympathy for the Sue, and torture often has that result. (It's also ethically a bad idea; the Sue may have no more sentience than the average insect, but just as it's distasteful to pull the wings off flies, it's distasteful to torture a Sue, and probably worse in the long run because Sues often mimic humans to such a high degree.) Forced retirement or even decommissioning usually happen, eventually, to assassins who lose perspective and begin to operate under the assumption that they are there to punish Sues rather than protect the multiverse.