Eh. Yes. It is something of an impossible challenge.
The closest I ever got was, I think, 134? I'm not entirely sure. (It may have been as high as 148 at some point)
It was pokemon Yellow, which helps enormously out of the first-gen games, because you get all 3 starters by default.
I did abuse the fact that I had both a gameboy colour, game boy advance, pokemon crystal, AND pokemon Stadium for the N64.
Basically, I've played through all of pokemon yellow 3 times, while keeping all the pokemon along the way by transferring them to another game and then back again.
(Yay for disposable magicarps.)
It's funny having two pikachus in yellow, and evolving one, even though that shouldn't be possible...
In any event, I think where I left it, I'll never get mew, but I do have 2 mewtwos and 3 evees, and all of the pokemon except I think I'm missing an omanyte for some reason that I can't quite explain.
In any event, Pokemon yellow and crystal overlap perfectly for the first 150 pokemon, which is oddly convenient...
But the omanyte aside, I basically have all the pokemon I would need to get to 150, but haven't evolved them yet.
Still, I gave up ages ago...