Geez, the WP for Koishi's Stage is ridiculously strict on Hard/Challenge and Lunatic. You have no power, you cannot really go unfocused since the Bakebakes slow you down if you try. Not to mention all the ghosts are pretty thick with the bunny's danmaku field.
I managed to get Komachi with Infinite Range + Waifu Parsee (replace your waifu chara here) to use FPM to take the Bunny out in 2 turns, while sending Aya up to the kendama to collect the bomb, that kendama is designed to be a troll, it always guards.
As for Koishi, it's a good thing she cannot do too much damage and her skill set is full, so she cannot even get Double Move on Lunatic.
Koishi has 2 blind spots on the map where you can sort of control how Super Ego behaves, but it still involves save scrubbing (50% that she teleports to somewhere you want). The first spot is to right on where Koishi starts, that waterfall is a backdrop and no one can go there, so I think the game will make sure she cannot teleport to there. The other is the southwestern edge of the map, but that involves Koishi taking a leisure stroll all the way down to you, which takes... a while, but that spot has almost no danger of her warping into the water, provide you started the fight on the southern edge.
And no, you cannot trap her. She always bypasses unit placement, cause lore.