Cave Story/Outer Wall

The outer wall is the means of access to the Plantation, the step before the doctor. Unlike other maps, gravity pushes items to the left rather than downward.

The booster V2.0 allows you to speed through the map without too much difficulty, otherwise, you will have to climb the wall slowly.

Nikumaru counter
If you didn't leave Curley to a watery grave (in the core chamber, her falling off after ironhead is supposed to happen) and have the Booster v2.0, then you can collect the Nikumaru counter in the room labeled with clocks. if not, the chest will not open. The counter is necessary if you want the third and best ending, so grab it if you're going for that.

Nemesis
Below the exit from the Egg Corridor, you can find a small dwelling. You need Booster V2.0 to safely enter, as V0.8 doesn't have sufficient control to enter or leave consistantly, although it is still possible.

This dwelling contains a few tiny people. The wife is looking for her husband who can be found in the graveyard. When you retrieve the tiny person and bring him home, you can optionally trade the sword for the Nemesis.