You have to get Marisa's items while avoiding the Shanghais and Alice. The trampoline has a limit as to how many times you can jump on it [indicated by the color it is]. Alice's and the Shanghais' use of the trampolines don't affect it. I think Alice opens the doors, however I'm not sure for I also am unadapt in moonspeak. D:
Well, it's a takeoff on the old Namco arcade game Mappy, and works in exactly the same way as that game did. When you pick up one type of item, you get double points for immediately going and getting the other item of the same type on that floor. The multiplier increases every time you do this, so you get double points, then triple, etc. The order you want to pick up the items to get the most points is: potion, book, broom, hat, and of course, Marisa's underwear, you sick fuck. Alice will randomly hug your items: you get a 1000 point bonus when you run into her then. Theoretically, the way to get the most points would be to wait for her to go after every item you want, and run into her. You'd be completely insane to do that though, so feel free to try.
You open the doors by pressing Z: they also kill any enemy following you. Doors with magic circles on them fire huge not-difficult laser beams that go all the way down the hall. You get more points for taking out more enemies at once.
Someone please explain what is it with Marisa x Alice? AFAIK, it's not in any of the games, and Touhou Wiki doesn't even mention it, yet half of the Touhou fanart seems to revolve around those two's relationship.
comment #34597 Fan generated couple I suppose. Kind of like how there's no idication of any subtle love between Ryouko and Nagato. However, people just group them together because they just seem to work.
comment #34576 Intarwebs for you. :3 The game is a lot easier with the ability to open doors/destroy the Shanghais~