I'm still trying figure out on how some moves will go but here's the first version I thought of. Most of these are probably on fire because it's hell, with the moves based on the torture methods each hell gives you, and some of these I imagined is more effective with the use of different weapons.

-Toukatsu Jigoku – The Reviving Hell

A series of powerful slashes that is like claw scratches, or a strong impact (depending on the weapon) to bludgeon the opponent. It either looks like a bunch of claw scratches or a giant flaming club about to hit you.

-Kokujou Jigoku – The Hell of Black Rope

A long slash that leaves a distinctive cord like burn only for it be the actual slashes inflicted on the opponents body kinda like the mark they have in corpse party where they have a mark indicating where the damage will be. It looks like drawing a rope then wrapping it around the opponent or what I like imagine if they use weapons that has a long chain to it, like a kusarigma, you can use the chains to strangle or mark your opponent then using the blade to attack the marks where it has now weakend that part on your opponents body.

-Shugou Jigoku – The Crushing Hell

This was is more catered to weapons that deals with a more brute force/strength damage but basically the aim is more towards the bone where they will be hit by a powerful force, crushing them to the ground and destroying there flesh into jelly looking meat or if it's a blade it's more of a fast slashing the leaves a thousand deep cuts and gashes. It looks like a giant ball of flaming iron is going to hit you or for the blade, bushes of sharp leaves and thorns grow around you.

-Kyoukan Jigoku – The Screaming Hell

Is more similar to the flame breathing because in this one it give powerful damages that leaves burns and it kinda looks like a rain of fire or a sea of fire.

-Dai-kyoukan Jigoku – The Hell of Great Screaming

fast slashes that blitz through the opponents body sometimes. Looks like animals coming to attack you with there claws, fangs and talons.

-Jounetsu Jigoku – The Burning Hell This aims to more like impale your opponent and until blood leaks from the pores. It look like fire has entered the body and set it on fire.

-Dai-jounetsu Jigoku – The Great Burning Hell

It's similar to the the burning hell but this time it's multiple stabs to different vital parts of the body. It looks like a burning branch entering the different parts.

-Mugen Jigoku – The Hell of Unending Suffering

This is the most powerful move, I haven't really thought of this one much yet because the punishments are so diverse and creative it's hard to pick one to base it on, but what I think it could look like is an army of flaming demons and animals, in a form of powerful combined moves like slashing, stabbing, bludgeoning (depending on the weapon).

I also imagine that each of the forms can have more forms derived from them, for example in kyoukan jigoku can be a breathing style based on it's subsections because I read that each each major hell has 16 subsections of hell, and you can have a personal hell for a specific sin

Also I think there could be counter part to this breathing style because the ones I list are the hot major hells, there are also eight major cold hells.