So this one is all over the place, but as whovian,wrestling,and DC comics fan I feel it would be interesting to see. So there are some things that go along with this.
2nd Doctor- is in his prime, probably from around the time he met Jamie. Towards the beginning of his run. No Screwdriver.
11th Doctor - this takes place from his time on Trenzalore, he's not in his advanced age but he's from that part of his time stream. He does have a screwdriver, however it is malfunctioning.
Undertaker- this representation is based off the character he portrayed, not mark calloway so he has some para normal powers along with his strength and dexterity.
Batman- this Batman is Ben Afflecks Batman from BvS.
They have 1 hour of prep time,battle takes place on the outskirts of Gotham