As some who completed this solo, and LEGIT, let me tell you that the word 'inconceivable' rings absolutely true here.
Previous guides emphasize using the 'co-op' method with main host being on Inconceivable and hanging back, while the second controller/guest player does all the dirty work on casual difficulty. Well, I'm here to give some guide to attempting this solo, LEGIT!
First off, you have to beat the campaign on Insane first before attempting Inconceivable. Now, I'm here to tell you that with a FEW exceptions, the Inconceivable run is actually easier than Insane in most parts for two reasons but simultaneously more aggravating as well: You have far less health than previous runs, but the enemies also have less health as well. You also get less ammo from ammo crates and from dropped weapons laying on the battlefield. So be wise with ammo and scavenge ammo from dropped enemy weapons and make sure your guns are as full as possible. Also trade weapons with AI allies when it's safe to do so.
Overall, I'd say this is more of a 'strategic' run and that it is easier in the sense that enemies aren't bullet sponges like they are on 'Insane'. However it takes far less damage to kill you so be very careful, especially during act 3. Also, you must make sure your shots count and hit your enemies too. They don't soak up bullets anywhere near as much as on Insane but they can easily mow you down with far fewer shots than even Insane so it's a very, very thin line between being moderately difficult and agonizingly nightmarish. It's your call.
USE EASTER EGGS!
The same easter eggs I mentioned in my guide for the Insane run apply here: Get Dom's Tomatoes and the Memento Mori but use them wisely! The former, I'd recommend holding onto until you get to the graveyard and use them to close up e-holes and limit how many enemies spawn. Then, shoot the gravestones in the correct order spelling MA-R-I-A and if it doesn't glitch, the scenery should turn very foggy and a heartbreaking audio clip of Dom contending with Maria being unable to be saved. After the gunshot is heard, a picture of Dom and Maria will fall to the ground and you'll pick up the Memento Mori.
As mentioned, you get 18 rounds, PERIOD and you cannot refill the Memento Mori so use the bullets wisely. You can instagib melee enemies to conserve ammo, even Pouncers (Be very careful doing this) when they're on one of your AI allies. I even managed to instagib a Snatcher who was in the middle of swallowing one of my AI allies though I'd be very, very careful about doing this. I mostly limited the use of ammo to against Carriers, the Swarmak, Dropshot Scions, and Snatchers when they swallow one of my AI allies.
That said, there are some extremely nightmarish areas that gave me rage-filled periods of grief: The Motorcycle section involving bringing down the plane, much of Act III, and the final boss.
The motorcycle section, do your best to avoid as many potholes as you can. If you have poor reaction time, you can do the pause trick method to see where the potholes may be and prepare to move accordingly. When you shoot the two engines and they explode, the plane doesn't go down right away. Keep shooting the damaged engines and eventually, they'll go out altogether. Then take out the turrets (They're almost tinfoil weak by comparison), and the finally take out the engine core, being mindful of debris and incendiaries falling out the cargo door. Also try to line up with the propeller when it digs a 'pothole' in the ground and stay roughly behind it at all times as doing so will keep you from hitting the ruts created by the blades. Once the engine core is destroyed and the plane goes down, you're all good.
Now for Act III, when you get to the Museum part, just try to kill as many enemies as possible when the teammates are using the turrets but when there are just a few or even one left, run back to the entrance you came from and when the Juvies arrive, they'll funnel down the stairs and if you're equipped with a Gnasher or even using the instagib melee with the Memento Mori, you can deal with the Juvies relatively easily.
If the AI don't go down on the third part with more drones, and you take care of remaining Juvies, this can be completed. It's still very hard and it's very easy to screw up and ruin it all.
The fourth part of Act III "Do Not Go Gentle" is probably the hardest part of the entire game, even with the Memento Mori as various rooms have pods on the ground that you can use as cover but be very wary of popping them as they could cause Juvies to spawn. Even worse, sometimes a loud shriek can be heard and all of the pods burst spawning an army of Juvies!
Finally, you'll face a combination of Pouncers and Juvies in the final room. This is where I first used the Memento Mori and killed all three pouncers, while either dodging or running in circles on the outside of the room, and funneled the Juvies so me and AI teammates killed them with gnashers, and/or lancers.
The final part, and probably the most grief-inducing area is the final boss, the Hive Mind on the final part of act V, known as "Release". I don't want to lie to you, this is hands down the area I had the hardest time with.
Part I/Flying pods: The first part involves pods erupting from the ground, and then flying right at you. Do your best to figure out the patters they spawn and as they open up, shoot them in the right sequence so they're taken out before they hit you. Just two or three hits are fatal. If you can take them out and not die, eventually, you'll reach the second and the hardest and most infuriating part of the entire fight.
Part II/Tentacles: Be prepared to die a lot, a LOT attempting this. First off, when he/she rises from the ground and his/her tentacles erupt, try to get as far back as possible and shoot at the tentacles, and land your shots as best as possible. Now the hard part is timing it to dodge the quills he/she shoots at you. He/she seamingly completely ignores the other mech that's with you and who sometimes actually blocks your path (Seething in anger), so would get as far back as possible. It makes it easier to dodge the quills though it makes it slightly harder to land shots as accurately. As usual, when a tentacle goes down, head up to it, and hold Y to staple it, cause it to break, and then when the ripped remains are withdrawn in, summon a rocket strike using LB to hit the tentacle crater and seal it permanently. Do this with the other three and then you're done.
Part III/ Severing the legs: This part isn't quite as bad as the previous part. First, you must tear the rotor blades from the downed helicopter and use it as a 'shield' against the pods launched from the Hive Mind's chest cavities. You must time it so the blades go full speed. He/she will fire three sets of pods at you. Make sure the chopper blades shred all three sets. Then advanced up, using RB to cool the rotor down. Then rinse and repeat with pods and when close enough, he/she will roar and attempt to stomp you. If you can get out of the way and not be killed, by the leg, you then use the Y-Button and sever the leg. Repeat this for the other one and when he/she falls down, just press Y and hold, and JD Fenix then slices the Hive Minds head and killing it once and for all!
Once that's done, you're all done!
Good luck to all who have the bravery to attempt this.