I'm looking for a word that would describe a third category following a "minor" and "major" category. (For compatibility reasons it won't do to insert a middle category of "moderate" or the like.) Example usage:
After fighting past several minor encounters, and a few major encounters, the adventurers finally made contact with the _____ encounter.
If it's implied that there are no further obstacles - final.
If it's implied that there's no greater obstacle - supreme.
If it's implied that there's no passing the obstacle - overwhelming.
If it's required to keep some kind of hierarchy - capital.
The word supreme is a good suggestion. You could also consider using ultimate:
greatest or most extreme
Final could be a candidate, too:
coming at the end : being the last in a series, process, or progress
[Merriam-Webster]
Minor and major are Latin comparatives for small and large respectively, so what is wanted is a superlative. I suggest supreme.
A musician, however, might suggest Dorian, Lydian, Phrygian, Mixo-Lydian, or Locrian.
Climactic or, as others have suggested, ultimate might work when referring to something that happens at or near the end of a sequence of events.
If you are looking for something in the middle or towards the beginning, prime is a good choice.
If you have a nerdy audience, which it sounds like you might, you could use boss, as in video games and tabletop RPGs.
If that's not the case, you might use final, although you would have to recast your sentence to avoid the repetition.
Consider, critical
Having a decisive or crucial importance in the success, failure, or existence of something ODO
After fighting past several minor encounters, and a few major encounters, the adventurers finally made contact with the critical encounter.
If it's the most important encounter in the series, and specifically the encounter that "matters" from a plot perspective, you might call it the primary encounter:
2 a : of first rank, importance, or value : principal
(Merriam-Webster)
Sticking with an adjective borrowed from Latin, in which language maior (= 'major') is a comparative from the root magnus, the English adjective formed from the borrowed superlative of the same root is
maximal, adj.
1. Of or constituting a maximum; of the greatest possible size, duration, or capacity.
["maximal, adj.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/115258 (accessed December 20, 2015).]
In your example sentence, this might be phrased as
After fighting through several minor encounters, and a few major encounters, the adventurers finally fought through the maximal encounter.
Because 'minor' and 'major' are adjectives in English (regardless of being borrowed from comparatives in Middle French and Latin, respectively), the superlative adjectival phrase
most major
is another possibility. This would be a rare use, but not unprecedented. Hence,
Their fighting ranged from the most minor to the most major encounters.
