To be honest I don't get why people are confused by the story either.
The overall arch is obvious - William (Sir Anjin) wants his spirit back that saved his life when he was a child. So it's important to him. Sir Kelley was commissioned by background characters (who will reveal themselves, keep playing) from England to go to Japan to acquire Amrita. A resource that William's spirit can find easily (like a compass, thus - why Kelly stole her to begin with). Amrita is a special resource that converts soldiers into demons (which the English wants to weaponize) - think the B.O.W program from Resident Evil (accept Amrita is in a sense, the T-virus). Amrita is in ample supply in Japan, which is why Kelley goes there with William's stole spirit animal. William thus follows him to Japan.
On the Japan front, you work with Hanzo who has recruited you to join with Ieyasu to control and unify Japan. William agrees because it allows him to track Kelley more easily. The characters you meet in the first few regions are simply various other warlards that Hanzo and you are recruiting. This recruitment also is further explained quite literally in a mission later on. For the most part in the first third of the game, you are in quest to meet up with Lord Ieyasu. Understand that the first time you meet him it's merely a body double to prove that William isn't an assassin. The secondary antagonist in the game can be seen as Lord Ishida, the strongest rival to Lord Ieyasu (the guy you 'work' for).
Williams crew consists of Hanzo, Okatsu, Tenkai, and Fuku. Your 'party' if you will that work for Ieyasu to assist you. The game begins to more focus on the primary objective in the second half, which the story becomes less about Japanese warring states and warlords and more about William's primary quest.
People had trouble following the story? Wut? It's super straightforward!
To add to what has been said, there was one detail I had missed, or didn't remember, from the intro mission in London, that made me go "ohhh right that's why". For a while I wondered why Kelley was so insistent on inflicting war and chaos across Japan, it just seemed like being cartoonishly evil for evil's sake. Now he IS cartoonishly evil too (he relishes in the chaos), but in the intro mission when you eavesdrop on his conversation (you can also peer through the keyhole btw and you see Kelley there but not the man he's talking to -- I missed the peeking part the first time, I just stood near the door to listen), and the man that sends Kelley to Japan tells him that he
must keep Japan at war because "blood needs to flow" to be able to unleash all the Amrita.
What I would say I dislike about the game are the sections where it feels like the game has imposed artificial, unfun difficulty for the sake of being difficult.
E.g. The area in region 2 with lots of instant death water holes and really tight corridors where falling to instant death is incredibly easy. Then in a side mission they fill it full of huge monsters with large AE attacks where dodging to avoid the attack is often instant death. My favorite was the standard demon soldier with an axe stood just in front of a shrine on a really, really tight form with instant death water all around - and he one shot me. That was a surprise. Camera weirdness + big monsters + narrow fighting spaces + lots of instant death terrain != fun for me.
I do really struggle with blocking. Whenever I meet a boss I cannot tackle (Dojo warrior adept mission, succubus lady etc) often it's because I'm not blocking enough.
Blocking helps in many places but I'm not sure Hino-Enma is a good example, I always focused more on dodging there, though blocking helped in a pinch for some of her attacks I guess.
As for the mission you're talking about, eh, I dunno. As soon as I saw a bloody grave with "drowned" I knew to be careful of the traps, and I almost never fell in the water because I proceeded cautiously the entire time. I don't see that as artificial difficulty at all, anymore than "having enemies that hit hard". It's just another obstacle to overcome, but instead of combat skills it's navigational and observational skils.
My problems with the game:
The story is terrible. I have no idea what's going on. They have some beautiful cutscenes, then ruin them by putting ridiculous info in subtitles. I can't read and watch at the same time! Then the story is just crazy, I have absolutely no idea what is going on or what my character's motivations are.
I'm not so fussed about it, I never really care about story much in games anyway, but I'd at least like to know what's happening.
The other problem is the way twilight missions work. I finally last night, had 2 twilight missions I hadn't done. I finished one, then I didn't have time to do the other. How long am I going to have to wait until it's available again?! Silly system IMO. I understand why they want to limit them - people shouldn't be compelled to do them immediately after finishing the original mission - but I don't like the system.
I agree the Twilight mission system is kind of whack, I don't care for it either. Plus sometimes by the time you get an "early" one unlocked, you'll be way overlevelled for it, which makes it rather boring.
That said read above for the story, lowhighkang_LHK summarized it pretty well, and I honestly don't understand why people struggled on this part. I mean it's a straightforward story, it's not exactly bad, but it's not particularly compelling either. It's just... kinda there.
Edit:
I also have a problem that Japanese names might as well be a list of letters and numbers to me.
Nobunanga? N120dgh7s is just as memorable. I just can't remember Chinese and Japanese names because they don't sound like real things. Just noise. It might help if I ever knew who the characters were actually talking about. I struggle to remember English names in stories when they're uttered and the character isn't present, so linking a Japanese name to a character and their motivations is impossible for me.
Um... wow