Pokemon Stadium - Petit Cups - Transfers ONLY from new game FAQ:

Q: What is this run?
A: Basically, only use transfers to beat the Petit Cups, while starting from a new file of Yellow. So you have to play through the game and build a team to the point you then beat the Little Cups.

The reason it is transfers only, is because otherwise the fastest method would be to to just use Rentals to avoid the team building altogether.

Run is also glitchless, as again with glitches you can very easily turn this into being completely uninteresting very quickly.

Q: How are you going so fast in Yellow??
A: That's the Dodrio Tower, a mode in Stadium that lets you play RBY at 4x speed, as long as it's connected with a transfer pak.

Q: Is Pokemon Stadium from a new save file as well?
A: No, otherwise you couldn't do both the Petit Cups without all the other stuff.

Q: Will you do a run of Complete Game with transfers from new game like this?
A: No, because grinding to L100 for Prime Cup would be insanely boring and not fun.

Q: Will you do other cups/parts of the game like this?
A: Yes, I've done Pika Cups, and Little cups in Stadium 2, and plan on doing some Gym Leader Castle stuff too.

Q: What is the route for the team you want to make?
A: There's a few routes I've had in mind, but the one I like the most at the moment is to rush a L30 Abra with 3 support mons, and 2 fillers.
So: L30 Abra with Psychic
L25 Eevee with Quick Attack, Body Slam, and Double-Edge
L25 Gastly with Thunderbolt (and potentially Self-Destruct and/or Mega Drain - though I'm currently unconvinced if getting these is worth it, especially Mega Drain as that takes a while)
L25 Horsea with Surf and Ice Beam
and then the 2 fillers, whatever shows up on Route 12 (could be Bellsprout, Oddish, Pidgey or Farfetch'd)

Other considerations that would be potentially useful are a ground type (Geodude/Cubone), but they are annoyingly rare and need some level grinding, and only helpful for electric types. Also considered a L30 Goldeen to use for one particular fight, but the stat requirements are a bit annoying. Also considered going Gastly to L30 instead of Abra, and giving it TB/Psychic/Mega Drain, but it's not as good as Abra for the actually difficult fights - though is better for a lot of the easier fights.

I would get Poliwag if you could fish a decent level one, but you can't until Route 23, and that requires the Rainbow badge to reach the water, which I'm currently trying to skip.

Q: Why Yellow over Red/Blue?
A: Abra is obtainable at a higher level is the main reason. Eevee also has Quick Attack at L25 in Yellow, but not in Red/Blue, which is also quite crucial in making the cup safer.

Q: Do you know if this will work?
A: Nope, just mapped out a general idea purely based on theory, I've done no testing at all. Given the nature of this run using multiple games and a transfer pak, the way to test this is with a run