It seems out of character for Alphys!Asgore to force himself to be important by throwing Shifty in a situation and lying about it for his own sake. He doesn't seem to be nearly as insecure as Alphys, either her canon version or her Storyshift equivalent. Instead, he creates the crazy scenarios for Mettaton!Undyne, so she can finally experience the crazy battles that she saw in Alphys's anime.
This would give Asgore a reason to constantly call them during their time in the Hotlands since he would be giving them a heads up on what he's preparing next.
At the end Undyne would discover that she had been tricked the whole time, and decide that she would have a real battle whether Shifty and Asgore liked it or not. For her honor, her spirit, and most important HER AWESOME VIEWERS!
- Unfortunately jossed. Asgore doesn't create scenarios for Mettaton!Undyne and only tries to help Shifty. Mettaton!Undyne's scenarios happen because her agent is desperately trying to have her do her scheduled broadcasts, but Shifty always comes at the worst moments.
Offensively, they'll use their magic, as well as "real knife" attacks. Since the latter type of attacks hurts Shifty's body, rather than their soul, they'll cut into their HP, and no amount of food will heal them.
So, how does Shifty beat Chara? Well, Chara will become increasingly tired as the fight goes on, so eventually, Shifty will be able to wrestle the knife from them and kill them with it.
However, since the characters who change places also keep the personalities and powers of their canon counterparts, we can assume that Undyne will still be as determined as her canon counterpart. Therefore, she would be able to assume a One-Winged Angel form similar to her Undyne the Undying form (Undyne ULTRA?), to put up with Shifty's attacks and the fight against her wouldn't be a Zero-Effort Boss like the one with Mettaton NEO. And maybe Sans, after losing his brother and all his subjects, could also act like his canon counterpart and give you a bad time.
Since Sans shares his canon counterpart's personality, he's probably as Genre Savvy and as aware of the mechanics of the game as him. Therefore, he may decide that the best way to end you would be to sucker punch you during your fight with Chara. The battle would start normally, until you're about to deliver the finishing blow. Then, if you choose to Fight to score the kill, Sans would come out of nowhere to kill you with his unavoidable attack. To prevent it, you would have to do something else (like Spare) or maybe a new ACT command called "Look out", that would only appear at that moment. Of course, just to piss you off, there would be no indication that a new action was available. Then, you would have to fight Sans and a weakened Chara together. Sans would be the main threat, with Chara supporting him with spells and knife throws. Once the King defeated, Chara would however become an easily defeated opponent.