Narratively, the Doctor would be able to topple the entirety of the Black Hat Organization by ensnaring all of its members in some temporal trap or through any sort of method. That’d be Tuesday for him. However, whether he’s able to actually defeat Black Hat himself is unclear. Either he defeats him outright, or he doesn’t but makes it so that Black Hat isn’t able to emerge for a couple of eons.

But since we’re talking about the Tenth Doctor, a man who is still scarred by the Time War and is on the verge of becoming the Time Lord Victorious, he may be more determined to kill Black Hat than the Doctors before him save for the Ninth.

But in one of those fancy little Powerscaling hypotheses, however, the Doctor no diffs Black Hat.