Take things slow. Don't go running in head first, hacking and slashing. Kite things down hallways, and use DA's charge to keep large groups away. Use a gun while you kite, to knock out some extras. Shield bump is your best friend. I spend more time shield bumping in particular depths, rather than actually attacking. Playing it safe will get you used to the stratum, and help you adapt to attack speeds and such. I had a very hard time with Trojans, when I first started soloing FSC.

Use Mist walls to your advantage. Stand on one side, with the trojan on the other, and when he attacks, run through the mist and hit it a couple times. Letting Trojans kill off Slags and such while you watch and laugh is a good strategy. Slow, but it gets the job done. In certain situations, where you can't play too safely, such as rooms filled with slags/closed gates/trojans/spikes. Well this is probably the harder stuff. If you don't use shiv, then kiting while using DA to push back slags, until you kill off a large number of them is ideal. Then you can work on the Trojan, so you don't have to worry about it anymore.

Use totems/wheels to your advantage. Blocking wheels in certain rooms with totems is very handy. In other cases, it's useful to sit back and let them do the damage for you, or even ignore the hoards of creatures coming toward you, and rush the wheels, killing them off quickly. That way you don't have to deal with both at the same time. Hugging the wall of the room is a safe spot from the wheels. If you hide there, you can safely kill stuff, and not have to worry about getting hit, unless you do a combo and end up sprinting forward, into the line of fire.

This is just stuff from my personal experience. Other people might have other advice, or other ways to do things more efficiently or whatever. But I took the time to learn this stuff myself, for the most part. By taking things slow in my own solo runs, without other people to show me what exactly to do. There are some "tricks" you can do, to make things much easier. But technically they may be against the rules, and I'm not going to share them in that case.

and yeah, generally people will use Vog, Owlite, Divine Avenger, a gun, and Shiv. Having Leviathan is always handy too.