Return to the Conduit to find a rocket platform in the middle of the path. Stand on top of it and examine it, and you will fly up to a new area.
The Egg Corridor is broken up into a front and backside, each of which are very similar to the other, with some minor aesthetic differences. On the front, Basil, the white wisp enemy, will travel along the bottom of the screen. On the backside, Basil will travel along the top of the screen. Contact with Basil will kill you instantly.
From the entrance, head as far right as you can. Enter the door to reach the backside.
Egg Corridor (Back)
Head back toward the left. When you reach the 'beginning' of the map, there will be a gap in the ceiling, allowing you to travel up and back to the right. Time your movement carefully to avoid the Basil.
When you reach the end of this sequence, you'll find a Save Room, with its own passages between the front and backsides. Stay on the backside for now, and continue travelling to the right until you find another door.
Head back to the left, and this time enter the bottom gap alongside Basil. Head back to the right and time your jumps over the Basil until you reach a small vent underneath the door you came from.
Egg Observation Room
Wait for the moving platform to move up a floor, then stand under it. Jump up on the left side to coax the Press to fall down, then dodge out of the way. When the platform comes back down, travel up the left side, then destroy the blocks under the other Press to get it out of the way.
On the right side, fall down and quickly fly to the left to reach the door back outside.
Head to the right, and be cautious of the spikes falling from the ceiling. When you reach a vertical chasm, wait for the large spike to fall first and destroy it before travelling up the gap. Continue to the right to reach a Save Room and the door out of the area.
Head to the right. You'll feel a chill...
BOSS: Dragon Sisters
Wait for either sister to open its mouth, then attack it. If you wait too long, the sister will spit fire at you.
After their health gets low enough, both sisters will open their mouths at the same time and spit fire at you together. Try to lure their aim in such a way that you can dodge more easily. Don't be afraid to head to the left or right sides of the area so the fires are coming from the same direction!
The strategy for this fight:
After the fight, a new door will open on the right.
Make your way up the wall, remaining cautious of the hopping enemies and the Night Spirits. Any patches of sand on the way up will contain a Sand Croc, so try to avoid contact with these traps, or keep moving to avoid taking damage.
As you get closer to the top, the wall will curve into a ceiling, and you'll have to do some tricky flying under and back onto the other side of the overhang. Be very careful when doing this, as if you fall from here it is impossible to save yourself without the ●MACHINE GUN●.
When you reach the top, enter the door to reach The Observatory.