A lot has been said about the increased significance given to Jessie and the rest of Avalanche in Final Fantasy VII Remake, but it's not just the game's NPCs that have been given the glow up treatment. Hell House can certainly attest to that. In the original game it could be randomly encountered in the collapsed expressway and didn't pose too much of a threat. In the remake, however, it's one of the toughest bosses that players will come up against.
It's challenging enough the first time around, but in Hard Mode, it's considerably stronger and has access to a few new abilities that can really turn the battle on its head. With the right setup and strategy and a decent understanding of Hell House's attacks and abilities though, it's a battle that can be navigated safely despite the huge step up in difficulty.
3 Setup
You'll want to ensure that Aerith has access to all four elements as she'll be dealing the bulk of the damage in this battle. Both party members should have Healing and Revival materia too and it's also worth giving Cloud Magnify and Time to cast Haste on the party and keep their ATB gauges charged.
Cloud should have Poison equipped while combining Warding and Subversion materia will grant him immunity to the Tonberries' instant kill attacks. The latter isn't necessary, but serves as a nice safety net. Give Aerith Magic Up if she has any slots left and fill Cloud's remaining slots with a mixture of HP and MP Up. Summons should be non-elemental; so Leviathan and Bahamut are typically the best options.
Aerith's best weapon for this battle is the Mythril Rod while Cloud's is either the Twin Stinger or the Buster Sword. As he won't be dealing much damage though, it doesn't really matter too much providing you pick something with a lot of materia slots. When it comes to accessories, the Gotterdammerung is a must if you have it already, but if not, give Cloud either a Champion Belt or a Circlet and Aerith a pair of Platinum Earrings.
2 Strategy
Phase 1
Have Cloud cast Haste and Bioga as quickly as possible and then use Aerith to lay down both Arcane and ATB Wards in the center of the arena. You're going to want to keep these up throughout the duration of the battle and so keep an eye on them and be sure to recast as soon as they run out. Have Cloud act as a distraction and only switch to Aerith to cast spells or let off a quick flurry of regular attacks to charge her ATB when needed.
Dodge and block attacks as required and have Aerith hit the Hell House's elemental weakness as often as possible. In the interest of conserving MP, it's best to use first and second stage spells rather than third as the increased damage really isn't worth the extra MP cost. Providing you're standing in the Arcane Ward when casting, this phase should be over pretty quickly.
Phase 2
Start the phase by recasting Haste with Cloud if it's run out and then have Aerith continue to use elemental spells whenever she has the chance. The Hell House will lose its elemental weaknesses for much of this phase, so it really doesn't matter too much which element you use. Fire and Lightning spells do tend to be more accurate though.
When the Hell House is pressured for the second time, use Cloud's Focus Thrust ability to increase stagger and then hit it with everything you've got once the bar is full. Other than that, you just need to make sure that you're killing any Tonberries as soon as they spawn in and keep both party members healed up until the phase comes to an end.
Phase 3
Phase 3 is more of the same, although be weary of Heavensword and Hellbound. It's possible to dodge the latter or even disrupt it by hitting the Hell House with its weak element in the moments before it drops. Neither are particularly easy to time, however, and so it's best to make sure that both Cloud and Aerith are fully healed just in case.
Once the Cutter and Sweeper are summoned, try to take them out quickly so that you don't lose track of the Hell House. If Aerith is doing okay for MP, now might be the time to use Thundaga just to speed things up. Once they're taken care of, the Hell House should be on its last legs and so just continue doing what you're doing and the battle should be over fairly quickly.
1 Hell House's Key Attacks And Abilities
Barrier Shift (Phase 1)
The Hell House will change its elemental affinity numerous times throughout the battle. Look at the color of its windows to figure out what its currently element is and then attack using the opposite element (if the windows are red you should cast Blizzard, if they're white you should cast Wind, etc).
Chair Salvo (All Phases)
The Hell House will fly up high and launch a barrage of homing chairs at Cloud and Aerith. The chairs can all be blocked and are a great way to charge your ATB gauges. In later phases it will use Chair Salvo Deluxe instead which works in much the same way while also adding ice cladding to the boss.
Firecrackers (All Phases)
The Hell House will release a bunch of toys which will explode after a certain amount of time or when you get too close. Just steer clear of them and you should be fine.
God House Mode (Phases 2 And 3)
A white shield will cover the main body of the Hell House which greatly reduces damage. Focus on its arms while the barrier is up or keep your distance and use this time to heal up. God House Mode will also add elemental cladding to some of its other abilities.
Heavensword (Phase 3)
The Hell House will fly around launching chairs and exploding toys throughout the arena. At the end of its countdown it will then use Hellbound; an attack that sees it slam down forcefully onto one of the party. Block the chairs and dodge the final attack if you can. It's not easy though, so be sure to heal up before the countdown ends. If you're able to hit it with its elemental weakness right before it crashes down it will cancel Hellbound; although the timing can again be a little tricky.
Hospitality (All Phases)
The Hell House will suck one of the party in through its door and bind them inside for five seconds. You should be able to outrun it, but if you do get caught, remember that you can still heal your trapped party member while they are inside the house. Hitting it with spells or abilities will free the bound party member faster. While in God House Mode, Hell House will use Renewed Hospitality instead, which works the same way while also adding a Wind cladding to the boss.
House Call (All Phases)
The Hell House will jump around the arena at random. It's fairly easy to get a good idea of where it's going to land and so be sure to dodge as required.
Housing Rush (Phases 2 And 3)
The Hell House will charge at one of your party members while flailing its arms wildly. Run and then roll either to the left or the right to get out of the way. In God House Mode, it will instead use Housing Shock and clad itself in Lightning before it charges.
Jetstream (Phases 2 And 3)
The Hell House will spin around in a circle and spray fire at the party. Providing you keep your distance though, you shouldn't need to worry too much about this attack.
Ram (Phase 1)
The Hell House will attempt to charge into either Cloud or Aerith. Run and then use the circle button to roll out of the way.
Rocket Charge (Phases 2 And 3)
Rocket Charge is fairly similar to Ram, although much faster and harder to dodge. The strategy remains the same though, but be sure to run left or right rather than forward or back. In God House Mode, Hell House will clad itself in Fire and charge twice in quick succession.
Enemy Summon (All Phases)
The Hell House will randomly release pairs of Tonberries periodically throughout the battle. They're not too difficult to defeat but can wipe out your party very quickly if left unchecked so be sure to kill them quickly to avoid their instant kill attacks. In phase 3, it will instead summon a Cutter and a Sweeper, so use Lightning spells to take care of them when it does.