I'm assuming the PS4 team has a level of about 7/8 the level of the WA4 boss they are fighting, given the two games' respective endgame levels. Obviously Rika a bit higher, Rune/Wren a bit lower.
PSIV (Lv 8) vs Earthbound Dead: Rika already has Saner! Saner overwrites Slow Down counters letting the PS4 team go all out then Rika to patch up their speed with Saner. Demi has Medic Power if Rika falls, Chaz can heal as Earthbound Dead tries to focus on her, it's all hopeless.
PSIV (Lv 10-11) vs Miscreation: Barrier stops Stone Bullet counters from being evil. But uh Stone Bullet is evil before they come up. Both bots have it at least. I think Miscreation guns down Wren first. Demi will put up Barrier to give her team a shot, so nobody can heal her and she as the only revier gets gunned down second. Rika uses Saner to speed everyone up, but Miscreation is still much faster. And he's still 3HKOing, and countering if a blitz happens. I think doing this carefully with lots of healing, and only Rune attacking, may work, but I'm not sure... Miscreation will poison Rune in his attempts to make sure Rune dies. But... PS4 can probably pull through, barely, only having Rune attacking when he isn't doubled? And hey Chaz can heal poison if need be!
PSIV (Lv 11) vs Jeremy Non (Rd. 2): Rika probably has Deban by now, lucky them. It doesn't matter much though. Jeremy doesn't instant double her so he guns her down. Demi can revive her, but he'll keep gunning her down, so they team is better off ignoring her. (This didn't work for Miscreation because gunning Rika down just leads to a horrifying Medic Power/Barrier/healing combo.) Still, the other three can unleash hell on Jeremy as he does this. And he'll get lots of doubleturns... heck, he instant doubles Demi and instant doubles her, by my numbers. I think PS4's fucked, here. He could miss some shots but eh.
PSIV (Lv 14) vs Belial: Oh geez. Okay. Belial again REALLY wants to keep Rika from getting a turn. 4D Pocket her right away, put up the distortion which only Rune can pierce (okay, Chaz has a single Airslash and Zan). Blitz out Demi. Blitz out Rune. At this point she'll probably have to 4D Pocket Rika again, but... she's making very clear progress. I just don't think she takes enough damage at any point.
PSIV (Lv 20) vs Kraken: Kraken's not fast enough to instant double or kill Rika, so she uses Saner. To make matters worse for him Psy equips aren't just storebought, but optimum defensive equips at this point, so Slumber Fog is out. All he can really do is try to clear out the water hex and then move there... but yeah, won't matter, Barrier happens, Deban happens. Slaughter.
PSIV (Lv 27) vs Balgaine Ales: Now PS4 has three revivers. If you guessed this would make Balgaine suck, well, you'd be right. (Yes, I let PS4 PCs use the hex system to stop his gimmick from working.)
PSIV (Lv 30) vs Super Soldier: Fails to instant double Rika, Rika gets a turn, Barrier happens, Saner happens, Deban happens.
PSIV vs Divine Weapon: Prismatic Laser causes misery and one of sleep/confuse/petrify which are all horrifying. This MUST get a Medic Power in response. Of course Divine Weapon is faster so on a doubleturn can try to Claymore or just kill Demi with something (non-fire damage not that great so this might not work). Though... apprently the PS4 team can go into form 2 with built-up CT, so Rika can go first, and they have a counter to this. Final form... also hugely problematic, if it gets Accelerator at the wrong time PS4 can get mauled, due to the actual MT. Eh. They could win this, though, which I wasn't expecting. Abstain for now.