I imagine a Deltarune PvP would have to be like a PvPvE situation. You would have the two opposing player sides fighting with their normal abilities, but there's also a Darkner(s) who aren't directly part of the fight but will be the ones attacking during the bullet hell phase of each turn, with both players needing to dodge. Perhaps there could be an ability or items that let's you change what the Darkner to hopefully get a bullet pattern that you're better at dodging than your opponent.
Actually, now that I've written it out, I've thought of an even better way to do it. Use the recruitment system to have players collect and maybe even train Darkners like Pokemon. When you get into a PvP fight, you take at least one Darkner with you. You and the other player use their normal actions to fight each other, but during the bullet hell phase, each player will have to dodge the other player's partner Darkner's bullet pattern.