You wake up in the Mimiga Village Lake without Curly (note that if you beat Ironhead without taking damage, you get a secret item). Don't worry, you'll find her later, but for now, it's time to get what most players consider the best weapon in the game. If you traded the Polar Star for the Snake or Machine Gun, you can skip this section; it doesn't apply to you. But if you waited and still have the Polar Star, then you're in luck.
First go into Arthur's house. If you jumped across the chasm in the Labyrinth, (meaning Booster is still alive) Booster will give you the Booster 2.0, which is mandatory if you want to get the third ending. Go back outside on the ledge just above the entrance to the reservoir and use two upward sprays of the Booster to reach a small block near the top of the Village. Jump on the blocks above it and fly toward the door and go through it. You'll end up in the First Cave. Now go see the gunsmith, who is awake this time. Talk to him, and he'll confiscate the Polar Star, but then he changes his mind and says you can have it back - after he's finished making it. Apparently, the Polar Star is an unfinished weapon, and the finished version is the Spur. This weapon is recommended if you want to beat Ballos. There are more enemies in the cave now.
If you got the Booster 0.8, you can get to the blocks up the village by jumping to the left from near the cage in which Sue was imprisoned, and boosting up while going to the left. This is not an easy jump, but it is possible. You can then go through First Cave to get the Spur (though you won't be able to get to Ballos).
In addition, you can return to the Labyrinth and head to the Gaudi shop and collect the Whimsical Star. This small item will orbit you (when equipped) to inflict minor damage.
You can also collect the Arms Barrier if you haven't already.
Once you collected the desired items, return to Arthur's house, and teleport to the Egg Corridor.
You warp to the Corridor, and find that not all is as you left it. The place is in ruins, with rubble and cracked eggs (plus the half formed, dead dragons that were inside) everywhere. Most of the enemies are the same, but watch out for falling spikes, they hurt. Watch out for the dragon zombies, though. They have long-range fire breath which deals heavy damage. Cthulu's Abode now has two Presses in it instead of Cthulu. Continue until you get to the egg monitoring room. If you collect the treasure chest in the middle, you get a 5 missile expansion and fight an optional boss, the Sisters. (Which also drops a save point) After the fight, proceed towards Egg Chamber #00.
This is where the game starts to branch. At this point, you see that Egg #00 has been successfully hatched by Kazuma, who shows up after you take a peek at the computer. After some depressing predictions about the doctor, he offers for you to escape with him on the dragon. If you say yes, you will get the first ending. Don't do that if you want to get the next (considered better) ending. Say no, and he'll present you with the final hope: if the core is destroyed, the doctor's plans can be stopped. It is a very risky plan, but, then again, this is a video game. If the odds stack against you, you can just start at the last save point. Kazuma proceeds to open a hidden door to the right, and goes through. Follow him to the outer wall.