Argue with the Sue that she can't logically have gone throught the rituals of becoming a Time Lord, therefore does not have the power to regenerate and thus is dead after being killed once.

(Keep poking me on that one. I keep being lame and hungover, and I can't beta worth a damn when hungover. Prod me repeatedly?)

Dalek.

Unless it's Uncle-Rusty-verse. Time was, The Doctor couldn't regenerate if the Daleks got him, I'm pretty sure. Force the Sue into sixties canon, one extermination should do it.

Seeing how the Daleks had this whole big war with Gallifrey, I'm pretty certain they have death-rays customized for preventing Time Lord regeneration. I mean, what's the point of exterminating someone if they get back up two minutes later with a different face?

Of course, Daleks are not the most reliable of allies. Maybe if you got your hands on one of their armor-shell-things and brought it back to base, someone could reverse engineer their death ray for missions like yours.

And then there's the obvious solution: dumping them down a black hole, leaving them at ground zero seconds before an A-bomb drops--you know, anything that breaks them down to their atoms. I'm pretty sure they can't regenerate from that. Of course, you might need a TARDIS to do the job.

Killing them thirteen times just adds to the fun! If you insist on killing them only once, I recommend something brutal that they couldn't possibly regenerate from. Decapitation, ripping out both hearts, incineration, etc. It may be hard to set up, but I doubt they could regenerate in a vacuum either.

Evidence from both the Old and New Series indicate that a Time Lord can't regenerate if the death is too fast. Witness the Doctor's drowning in Turn Left, or the shooting of the Castellan in Five Doctors.

The Doctor has also been in danger of permanent death from having his brain burnt out (Forest of the Dead), and according to the Tardis Wiki, you can kill a Time Lord by stabbing both hearts simultaneously. Or you could just make them not want to regenerate (Last of the Time Lords).

To be honest, regeneration is one of the least useful aspects of Time Lord-ness. There's just so /many/ ways to stop or disrupt it; the Doctor worries about dying practically every story.

hS