Not only did I beat Culex, I beat him the second he was available to fight! And I'm pretty sure they intended you to beat him after you beat the game.I had to use pretty much all of my OP items (2 red essences, 4 Kerokero Cola, 4 Royal Syrups, etc.), spam Come Backs and Pick Me Ups, and it took a few resets but I did it. Honestly once his 3rd crystal went down the fight was relatively free from that point. Although even on my successful attempt Peach was down and I was out of PMUs and this happened when he was one or two more hits from going down. If it had gone on for two more turns I would've lost on that attempt
Sorry if this is a bit of an annoying post but I wanted to brag about somewhere.