So I'm not entirely sure how the Legendary Enemy system works, but I wanted to make a quick note of this as there may be some confusion based on things I've said in my other post.
It seems Legendary Enemies show up in one of two ways:
(DISCLAIMER: This is purely from observations of my own and could be 100% wrong)
A) Legendary Enemies can have static, fixed locations in key areas and will be a mandatory required kill in clearing areas. So, for example, if you loot a bunker base, the Leg enemy could be waiting for you in the final room and if you Save/Re-Load on death or w/e, he's still there waiting every time. He's not optional for clearing it and you'll always get to fight him.

In the wild, there are "random spawn" enemies that just appear in certain places, unpredictably. These enemies can be Legendary and the chance to find them scales with difficulty. In my experiences, these enemies DO NOT REMAIN on reloads, as it seems the "random spawn" enemies reset with each loading of the game world. I admit, I have not had an instance where I was able to save so close to a Leg Enemy as to immediately load and check this theory, but I can safely say I have died to Leg enemies, respawned, immediately gone back to fight that enemy and found they have vanished completely.
As far as A) goes though, I have some other observations on that too that could further modify this theory.
So sometimes when you go back to areas you've cleared, they'll be completely full again with enemies, and when this happens the containers and everything will also be re-filled with loot. This means the game is never truly empty of enemies and it's never "beaten" - you can always go back and re-complete mini dungeons. Now, when this happens, every enemy tied to a location is static. Every time you load/save, they are exactly where they were, if they're tied to the place you're at. This includes Legendary Enemies. So I'm not sure if they're static in that they'll ALWAYS be there the first time you engage a zone, or if they're just a "random" spawn in the pool of enemies you rolled when you showed up to that zone, or what.
My point is, Bunker X may have a Legendary Raider the first time you clear it 100% of the time, or it may not? I don't know for sure, but you WILL find Legendary enemies inside areas that can be fought multiple times.
I say this because I made a comment about how "Legendary Enemies are do or die, in that they won't be there when you respawn." This was meant to refer to the ones spawned by method

, and should not be confused with static enemies.
Also, I've received a lot of questions about "Do legendary enemies have special moves?" The answer is, sort of. Every now and then, you'll be fighting one and upon damaging it, if you don't kill it, it will pop up a message that says "Legendary Poopsmith has Mutated!" and suddenly they get this crazy aura around them and will now likely one shot you. I've always checked to see if they do any cool animations like grow extra hands or heads but it always just looks like this power aura. It seems to happen a lot when I use a Critical on one and don't kill it. But yes, this happens frequently and waaatch out, they wreck when this happens.
Anyhow, Difficulty may affect the static spawn chances or it may not, but from my experiences it DEFINITELY affects the open world random encounter Legendary chance.