The most useful ability of the fighter is Veteran, which allows you to level up more quickly by gaining additional experience. This will be important, since the fighter has a very hard time fighting enemies that are a higher level than himself, and will therefor be missing out on bonus experience. The Instinct ability will occasionally prove helpful to save on exploration space at level 1, but this won't help if you're searching for anything other than an equal-level monster.
Despite the usual inclination from fighters, you don't actually need to play them like a physical powerhouse. You can play them as a hybrid build or even as a magic-user if you're so inclined. The fighter has no particular class features that make him favor physical over magic damage, so always try to play with maximum flexibility.
Race and Deity Choices
Since fighters are so flexible, any race (except maybe Goblins, since the fighter gets extra experience) can work well as one. For new players, though, human and dwarf are probably the better choices, with humans for players who prefer offense and dwarves for defensive players.
Likewise, deity choice is pretty flexible. As always, the The Pactmaker is a good catch-all deity, and the others can fit your situation as necessary. Jehora takes your death protection, but if you've already used it that's not an issue. Likewise, Glowing Guardian can grant extra death protection if your first one runs out, but that Piety is usually better spent on the Healing boon (unless fighting Gharbad). Fighters really only have to worry about the dictates of the dungeon and a player's given style, so as with race, you can make any god work for you.
For this challenge dungeon you should strongly consider a more exotic Fighter race. Elf is a great option, as you'll want to rely heavily on BURNDAYRAZ to soften up the many monsters that punish melee attacks, and buffs like GETINDARE and BYSSEPS to deal the killing blow. HALPMEH or the Halfling's ability to convert glyphs into healing potions can also help to cure poison between fights. As always, use your INSTINCTS to guide exploration. Focus on Serpents and Gorgons while leveling up in the beginning, and set aside some lower-level Nagas for mid-fight leveling against the bosses. Try to save your free death protection for the fight against Medusa unless you luck out and find CYDSTEPP. Leave Jormungandr for last.
Consider using a Dwarf here, as the extra max health really helps against the hard-hitting Warlocks and Aequitas. Finding a source of magic resistance will also improve your chances. If the map spawns high-level monsters blocking all early exploration routes, attack one of the Imps to make it blink out of your way; your death protection will let you live to explore the new route and hopefully salvage the run.
Trying out an Elf Fighter is a very viable option. Due to the high physical resistance of the Tormented One, you'll have a hard time beating him as a (typical) Human Fighter (unless you can change you physical attacks to magical ones in a shop). As an Elf Fighter you'll get a significant Mana Boost, that will help you beating the Tormented One with fireballs and midfight leveling at level 7-9. Due to INSTINCTS you should be able to conserve many tiles to regenerate afterwards and face Frank, who can be outlasted, if you have piled up some health potions. A Goblin Fighter may be an option too, as it eases midfight leveling, but you'll be unable to use fireballs that much.
Having the Glowing Guardian as a deity is good, because you can take two more heavy blows for free. Taurog may power you up, but forces you to not use fireballs effectively, which are a big help. Tikki Tooki is always an option, since an extra potion and Dodge Bonuses can never harm. IF (!!!) you manage to get fireballs and Mystera Annur early on, you can try to beat the crypt as a mage. Finally, Jehora is a good option too, especially if you happen to find WEYTWUT early to pump piety quickly, because for 50 piety you will transform both bosses to something less problematic. Maybe.
It is also important to try to beat high level monsters while leveling up to level 7-8. It will make midfight leveling with the bosses easier. A combination of fireballs end HALPMEH as well as clever handling of tile regeneration will help beating monsters 2-3 levels above your own level.
Much like the Crypt and Snake Pit, an Elf Fighter may have the easiest time in the Factory. Locating BURNDAYRAZ early is crucial, as you must leap up to higher levels by destroying very-high-level Animated Armour with it. BLUDTUPOWA will cut down on the amount of tiles you need to explore to do this. Allow yourself to take out level 6-9 Golems when possible. Of course, unless you can located HALPMEH or CYDSTEPP you probably won't be able to win, as at least one of these is practically required for the Boss fights.
Take the Iron Man first, which should be simple if you have either CYDSTEPP or HALPMEH. Super Meat Man is more challenging, but if you've followed the above strategy then the dungeon will now be littered with low- and mid-level monsters who can be taken out for huge chunks of experience. This means you can probably level-up twice during the fight with the Super Meat Man, enabling you to maximize your efforts. As always, if APHEELSIK is found and there are enough tiles left, consider picking it up for this fight.