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Lads, I just beat the champion in HC rad red with soft nuzlocke rules.
I think this is probably theoretically possible? Though Lorelai is actually fucked up with two entirely different teams that can't be solved with a scarfed u-turn lead like every other E4 member. And then if she doesn't kill you, Bruno will almost definitely wipe the fuck out of you.
My E4 team was Aegislash, Snorlax, Terrakion, Landorus, Latios, and Darm-G. The good news about this team is that it's extremely "consistent", 5 of those are guaranteed encounters. Bad news is that Terrakion/Latios are near impossible to catch due to the abysmal catch rates in this game, I had to cheat and reset until I got them. That said, I do think Latios is fairly replaceable, and same with Terrakion to an extent. Landorus is near required imo, but it's also literally guaranteed because you have a Master Ball. Darm-G was an insane encounter though, and I think if you don't get him you'd probably have to change out at least some of the other 5. Additionally, all 6 of those are relatively late encounters, so I think you should be able to get to the E4 with them pretty consistently if you can catch them at all. Snorlax and Aegislash kinda don't fall into that category, but if they die earlier on, your run is probably dead anyway I think.
If anyone has any thoughts on the game I'd love to hear it, because I don't think I'm even going to attempt a single actual run. I just don't think it's practically possible.
Pic related is me ranking every important encounter I got. Gastrodon is mostly just as good as Aegislash imo, but doesn't do anything for the E4 so it's slightly worse.
Side note, fuck the captcha, it doesn't work on 4chanx.