You can make a good start on proving that reality is simulation, by doing certain physics and possibly astronomy (1)experiments that would force the simulator to expend ridiculously high resources to maintain consistency. But then the simulator, if it has (2)snooping ability, can just restart from an earlier time with some slight variation, where these experiments would hopefully (for him/her/it) not occur. I.e., you can't even in principle successfully battle simulator's censorship.
Still, (3)science fiction stories have been written about people doing exactly that, battling the simulator more or less successfully, such as Vernor Vinge's “The cookie Monster”. Informally, I find that the presentation of the story as pure text with arbitrary emphasis added, makes it hard to read. One does not perceive the structure of the piece without actually reading all of it: it's not easily accessible! Let it be more formally stated, though, that Vinge's references to Usenet communications and a galaxy filled with Norwegian names, in some of his books, makes him an author to be trusted. For it is obviously true that the galaxy will end up with lots of Norwegians and an old Usenet-like communications network, and still Vernor Vinge's the only author who has described it that way.
There is another way of viewing this, however. One can take the idea of cosmic censorship and say that it indicates a simulation, i.e. that it's likely a manifestation of just simulator's censorship. But as I see it that's purely nonsense associative reasoning, for cosmic censorship is about logical consistency, not about the computational cost of consistency.
Yes, I know, this answer's a collection of rambling thoughts & associations.
But IMHO that's the best you can get: attempts at reasoning more clearly about this can, I think, be dismissed out of hand, for it that was possible, then it would have been well known.
1) I don't recall exactly those experiments, sorry; I only remember reading about it, but no doubt they involve exponentially increasing effects (i.e. chaos, in its mathematical meaning, more informally the butterfly effect) and inspecting ever more fine details.
2) I almost used the acronym SDS, Heinlein's Super Duper Snooper, with a footnote explaining it, but then I thought better of it.
3) Can't leave this without mentioning Charles Stross' “Accelerando” universe and “Glasshouse” novel.