I'm pretty sure this is everything, someone let me know if I forgot something.
Step 1: Prevent Curly's death. You don't have to do anything for this until you get to the first battle with the Core. Before speaking to her in the final room there, find the Tow Rope which is sitting on the ground on the far right side of the floor. After the fight is over and she gives you the air bubble, use the rope to carry her body.
Step 2: Take her to the little cabin in the waterway. For some reason I have a hard time with this part; I often miss the jump to the cabin and there's no going back to it once you miss the jump so you'll have to reload if you screw up.
Step 3: Drain the water from her body. Put her in the bed, then read the computer and bookshelf in the cabin a few times until you learn how to do it. Make sure to take her with you when you leave. Her body will be swept away when you beat the fish, but she'll survive.
Step 4: You know the part where the Professor is at the bottom of that shaft and gives you the Booster 0.8? It's difficult, but it is possible to make the jump across that chasm without any boost. You can use the machine gun if you have it at lvl3 but if you want the best weapon in the game you won't have the machine gun at this part. If you do this right you'll get the much better Booster 2.0 from the Professor before you return to the Egg Corridor.
Step 5: In the Outer Wall there is a not-so-hidden room which contains a timer item. I don't know if this is actually mandatory but if you can't get it then you know you screwed up somewhere.
Step 6: You'll find an amnesiac Curly in the Plantation. Talk to her and the Cthulhu with her a few times until he tells you what you're supposed to do.
Step 7: Go back to Mimiga Village (teleport shenanigans make this faster) and fight the Ma Pignon mushroom in the now-accessible room inside the graveyard. He'll give you a bum item at first so check your inventory and look at the item, then talk to him again.
Step 8: Bring this back to Curly. Talk to her a few more times, at which point she'll reveal your character's name (if you don't already know it), and give you the Iron Bond. If you have that and the Booster 2.0, then you should be good to go. You'll know you did it right if the "Final Cave" or whatever that's called after you ride the elevator thing is a different, harder room than before.
Step 9: During the escape after beating the Undead Core, go inside that little building. There should be a hole in the floor which will take you to the final area. Good luck!
As for the best weapon in the game, you need to not trade with Curly, and then don't speak to the cockroach guy sitting at the store counter in the labyrinth. If you return to the Merchant whom you first stole the Polar Star from once you can get there (via Booster), he'll upgrade it to the Spur if you still have it. If you talk to the cockroach guy instead, he'll give you a different weapon but it's not as good. However, if you talk to him after you get the Spur, he gives you a different item. It's not super-useful but it does help a bit.
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(10:17:09 PM) Ed Bellis: i think pac-man just keeps repeating, for instance
(10:17:26 PM) ertyu: ya well tell that to billy michtlle