Two kids no brane
You can probably pull it off with Kadabra too, since iirc his SpAtt and Speed are comparable to Espeon's. He would just be a little more fragile. Plus it's tougher to get an Abra (unless you buy one from the Game Corner, which would require long hours of Voltorb flip) than an Eevee.If you can trade-evolve and are willing to give up Eevee (or get insanely lucky), Alakazam does even better since it can learn Psychic before level 50 IIRC.
In other news, still grinding -_-
I mean really there's lots of options, some probably even better than Espeon, it just happened to work really well for me so I posted it. Karen is going to be rough though, let alone Lance. Especially with no restarts or healing, ugh. And I have to do it all with a L43 Crobat, L44 Feraligatr, and L45 Ho-oh. I have a feeling I'ma need some serious luck on my side, or maybe a sacrifice or two.
Does Nuzlocke include Kanto and Red, or just the E4? My strategy might change if this is the case.