From experience, a perfect battle with three outspeed-OHKOs takes just under 2 minutes from the start of one battle to the start of the next.
Pika Cup - 8 battles, and the opponent doesn't take advantage of the min-maxing possible with level spreads (or very much in the way of low-level EV training) to the same extent you can, so a fully perfect cup is quite possible here, and a time of about 16 minutes including the award ceremony at the end
Petit Cup - 8 battles, still offering a min-maxable level spread but it's not quite as noticeable here (the difference is only 20% tops, as opposed to the 33% in Pika, but since level manifests itself on a quadratic scale, the differences are effectively 44% and 78% respectively), nor is there as much in the way of high-BST mons available to use. You can still sweep most of the cup fairly handily, not quite as easy to reach total perfection in this cup but certainly a performance in the 16-18 minute range is expected.
Poke Cup - 32 battles, and the level differential by this point has shrunken to almost nothing. If you want to assume TAS luck, then the answer is trivially "spam Fissure and Horn Drill on everything" and the run isn't very interesting at all; otherwise this is where opponents start to get bulky enough, particularly in the upper quadrant, that sweeping everyone with straight OHKOs isn't an option, so you'll need a bit of setup and/or switching for matchups. Just as a guess, I'd put up 18/20/24/28 minutes as par scores on the four quadrants; that'd make 90 minutes for the whole cup which sounds spot-on.
Prime Cup - 32 battles, probably a bit easier than Poke Cup since you get to use Amnesia Mewtwo to just blow everything away, which you couldn't before. Setting up the Amnesia in every battle takes a bit of time, but it should generally be an improvement over anything you could do with a L55 sweeper, so 80-85 minutes for the cup as a whole sounds right.
Gym Leader Castle - 37 battles, shaping up to be a lot like Prime Cup in that Mewtwo is still eligible. The opponents do spend considerably less time with "Poke Ball-level" teams, and there are more intermissions where you have to reselect a team, so this should take longer on average, but not too much so. Let's call it 95 minutes, maybe 96 factoring in the cutscene at the end where you get a Pokemon Present.
Vs. Mewtwo - 1 battle, really easy. Bring Snorlax and Selfdestruct on turn 1; if it survives that go to Electrode and Explode on turn 2 before Mewtwo can ever move again; that's a guaranteed 2HKO and then you have a Magikarp in the back just so that you win instead of lose on a double KO. Easy 1:30 plus however long the credits take.
Adding in some wiggle room for when things go wrong like an unlucky freeze, that still puts all of round 1 between 5-5½ hours. Round 2 is pretty much the same but the opponents are a bit more competent and bulkier. The lower level cups aren't impacted as much, and the same 2-turn plan vs. Mewtwo is still guaranteed to work, but Poke and Prime take considerably more effort to break through (particularly Poke, where again you don't have Mewtwo to help, but the team developers learned their lesson and shuffled the trainers around so that position 8 is no longer "Old Man with a balanced team", but rather "JUST SPAM PSYCHICS"). That could push the totality of R2 up around 6 hours, but the whole game should be able to stay under 12.
