If you have the Machine Gun on level 3, boost upwards by firing it down.
There are several ways to get to the door: I was in Labyrinth B, looking for a power source of sorts, and I thought I'd done everything there needs to be done in the general neightbourhood, zealously saving after each event. Well, five minutes ago I got stuck for long enough in Cave Story+ to finally fire up a walkthrough for the game. It's very difficult to explain without any spoilers, but it involves skipping certain events and items to get better items at a later point, and making sure you follow through on an optional sequence of events. The best ending is achieved by following specific requirements at certain points in the game. Grace Note said, in an answer I hadn't read until it was too late:
