The Island
Sure thing.
First and foremost, this is the Island. I don't think it's possible to determine it's exact size, but it is at least as big, if not bigger, than all of the zones combined:
First Cave
Mimiga Village
Egg Corridor
Grasstow
Sand Zone
Labyrinth B
Labyrinth H
Labyrinth I
Labyrinth M
Labyrinth W
Labyrinth - Core
Waterway
Outer Wall
Plantatio
Last Cave
Balcony
Sacred Ground - B1
Sacred Ground - B2
Sacred Ground - B3
While I was adding these, I realized that you might be able to calculate the size of the Island by using the Outer Wall. Not sure though.
Anyways, the Core is the force holding up the Island. After defeating it, Misery will teleport to the scene and state that the Core is the "heart if the island" and that "if you stop it, the island will fall to the earth":
https://www.youtube.com/watch?v=idJjPjQ0XQw (she says it around 2:45). The Doctor then teleports in as well, telling Misery to bring the Core to lab via teleportation while there is still time, which she does.
Later in the game, after defeating the Undead Core, which is the body of the Core possesed by the Doctor, you wake to find that the Island has begun to collapse. After running and jumping off of the edge, a brief cutscene is shown where the Island falls to the ground:
https://www.youtube.com/watch?v=zJHV-zz5O1A (the Island falls at around 2:07).
Now that that's out of the way, let's move onto Ballos.
Ballos is the true final boss of the game, only accessible with certain requirements. While going through his stage, the Sacred Grounds, a narrative will be displayed along the bottom of the screen. It tells us that Ballos had magical powers, which he used to protect his people. The king was jealous, so he imprisoned and tortured Ballos to the point where snapped, and destroyed his entire kingdom with magic. I couldn't find any scans/videos, but you can read both translations at
http://www.cavestory.org/game-info/theory-reference.php The narrative is at very bottom of the page, and the kingdom-destroying part is under "Hell Narrative Part 4". Both translations pretty much say the exact same thing.
Also, it never really specifies how big the kingdom actually was. The definition of a kingdom, according to a quick Google search, is "a country, state, or territory ruled by a king or queen". What would this be then? Would it be at least Small Country Level or something along those lines?
Anyways, those seem to be the strongest opponents that Quote has fought with and beaten. Time for some speed stuff.
As mentioned above, there are multiple instances where Quote dodges lightning. The first one is during the Misery boss fight at around 1:59:
https://www.youtube.com/watch?v=RNt2RWBBKeI
The second one is during the Ballos fight at around 1:15:
https://www.youtube.com/watch?v=VwqQY7n9r2s
There is another one, during the fight with the Heavy Press, but I'm not sure if it counts, as it does come from a machine. It's around 6:25:
https://www.youtube.com/watch?v=rOwAXABuej4