As I said, it's a theory that spans from chapter 93 to chapter 95. It all starts from this panel:

Yukio's -determined- look (that's how I want to call it and I'll explain why). Let's start from here. What happens in chapter 93? Yukio hits rock bottom. No matter what he did or how much he achieved during his (exorcist) life, he thinks to himself: "I was weak (when I was a kid) and I couldn't get any stronger"=I was weak and I'm -still- weak=everything I done up to this day was useless=I'm tired of struggling=I give up=I want to die.
He's lost all his will to keep pursuing his biggest (and the fact that he would wish to kill himself 'cause of his "failure" prolly proves that this was also his -only-) objective in life: become stronger (than Rin). He points his gun at his head and pulls the trigger, only to have Satan burn the bullet, call him a "weakling" and a "fool".
Now, back to Yukio's close-up panel. I stared at it for a while and asked to myself: considering who's Yukio, that glare: does it really look like it's coming from someone who's thinking to himself "Okay, so I can't die. What I'm gonna do now? Oh, I got it. Let's make a (foolish) last stand and go ask Mephisto for infos I know 100% he will never agree to give me. After all the times I declared I'd never accept anyone's help and I'd never go ask anyone for advice, am I going to start now 'cause I'm -that- desperate?" or "Okay, so I finally discovered who's in my eyes. And from what Satan said, it looks like he needs me for something. Oh, hi there Shima. That's right, the Illuminati are after me too. Now, I have all these infos. Let's come up with a way to use them at my advantage. Sheesh, Satan's right... I really am a fool. I may be weak but I'm smarter than this. Let's put together a plan."
Now, the thing which bothers me: we can safely state that Yukio tried to shoot himself at around 7:12/13 am. Next time we see him, it's around 11:30 am. First of all, I found it weird that Kato-sama suddenly started showing us at -which- time -what- happens. Maybe there's a reason behind this?
So, on to an analysis of chapter 94. We're shown only one panel about what happens after Shima shows up in front of Yukio (Yukio "taking" Shima down). But, that technically happened at around 7:30, right? And Shima is calling Mephisto to warn him right after the press conference's started. Isn't it weird he waited for 3 hours before making that call? Were both his arms so weakened by Yukio's grip that it took him 3 hours to recover a bit of mobility? And there're also two other weird things to consider. Before Mephisto hang the call up Shima was about to add something else. AND let's not forget Lightning got some plan of his too. At the beginning of chapter 94, he weirdly states "I hope nothing -unexpected- happens." while facing away. Also, the fact alone he'd brought up the barrier matter in -that- moment out of all looks... um...
What am I getting at? I have the feeling Shima, Lightning and Yukio may have a connection of some sort.
Back to the press conference. Mephisto turns to find Yukio there. Yukio starts questioning Mephisto about what he knows. About his eyes, and so on. And, the eyes are conveniently Satan-shaped to help him make his point clearer. Mephisto eventually refuses to answer and proceeds to provoke him right after Shima warned him that Yukio was about to break. Like, so he's about to break? Let's give him a final boost.
Next step: Mephisto begins to talk and Yukio is at his side. I'm assuming -Mephisto- absolutely knew that Yukio would've tried to shoot him at this point AND that he was gonna do it right there, in the middle of a press conference on a live broadcast. Here I'm assuming this was -still- all part of Mephisto's plan. He needed a reason to compromise Yukio and get him confined without looking like he (Mephisto) was the one behind it. As for the objective of his plan... well, whatever Mephisto could gain from that.
But, here's where Mephisto's plan fails. Tell me what you want, but a coincidence as big as someone randomly shooting Mephisto from the audience 1 nano sec before Yukio pulls the trigger is, imo, too "stupid" a clichè for Kato-sama's skills. So, what I think is this: it's -actually- all Yukio's plan.
One step at a time: Mephisto wasn't randomly provoking Yukio. He totally expected him to shoot him. But, he didn't want to lose his body -yet-. So what I think Mephisto was planning is: "The moment Yukio will shoot me (from the side) I'll use my time/space skills to reduce the damage/camouflage the shoot which will come from -that- side." Something like putting on a barrier to his right temple to decelerate the bullet speed and reduce the -strength- of the impact. In other words, he was planning to take the shot but not to let it damage his body in a compromising way.
But, surprise surprise, the shot came from the front side. Something he totally -didn't- expect. So, the damage was higher 'cause he wasn't ready to protect himself from that side. And this would explain the surprised look on his face. But Yukio looks surprised too, nah? And here's where I'm gonna connect this episode to three of the facts I listed at the beginning of the post:
-Yukio's battle against Todo.
-Yukio using the nutrient bullets trick twice. ("Can't you do anything else?" (Rin))
-Yukio's infamous ability to fake emotions to his advantage/convenience.
Now, a lil step back: during the fight against Todo, before the BEI. Here's what happens: the pattern is similar. Todo provokes Yukio. Yukio "lures" him into believing that he's falling into his trap (it's arguable that Yukio is prolly only -half- faking his emotions during this part, I know). Todo even comments "You're not hitting anymore. Your heart speaks the truth." 'cause he -really- believes Yukio's NOT missing him on purpose. Yukio successfully tricks Todo into believing this. But, Yukio was -not- randomly shooting, he was setting up a magic circle. And once all's ready, he smirks at Todo. I also noticed these two panels:

In this case, we're never given by Kato-sama any hint about Yukio's plan. We're tricked into believing what Todo believes too until the plan is complete. 'Cause that's Kato-sama's choice. And that's another reason why I think she may be avoiding to put any panel that could hint to a possible Yukio's secret plan on purpose. Like she did back in that chapter.
The second fact is: as Rin pointed out, Yukio used the nutrient bullet trick twice. It made me wonder: so is it possible that Yukio's recycling the same pattern of actions again to trick Mephisto? It worked quite well against one hella good mindfu*ker (namely Todo), so he may have thought it was a good plan to use against Mephisto as well.
Now, back to chapter 94. Who's the shooter than? I'm guessing someone like an ally Yukio assigned the task to shoot Mephisto. As I said, we got 3 hours from the moment Yukio tried to shoot himself and the press conference began. So, that's quite a long time to organize a plan.
If so far I'm right, than this could explain Mephisto's words: "You never know what humans will do, that's why they're so interesting." while he's staring at Yukio. Mephisto can't be talking about the shooter. He's talking about Yukio. By this time, Mephisto saw through Yukio's plan and he's "complimenting" how smart it was of him to think/execute this plan to trick him.
But the plan is not over yet. And now I think it's a good time to talk about something else. Okay, if Yukio really got a plan: what is he aiming at?
Oc, his undying wish: he wants to become stronger. And here's where I'm gonna connect another fact:
-Yukio's plan to trick Hachirotaro into shifting Shura's regenerative ability/demon sword contract to him.
Let's take a few steps back. As I said, Yukio may have thought to himself after hearing Satan's words: "It looks like he needs me for something, that's why he's keeping me alive." I can think of Yukio using this to his advantage. And I can picture Yukio making some sort of "pact" with Satan to get (in exchange) something from him: I guess, power. But, it's a pact (and Yukio's darn good at making those too) so Satan has to gain something from it too. Okay, so what could Satan possibly want?
In chapter 1 Satan makes it quite clear: "Assiah will be mine!" "I need -you- (Rin) in order to lay claim to this world!". So, basically, he plans to do something to "conquer" Assiah AND Rin is needed in his plan. Plus, he may need a body capable to sustain being possessed by him for a very long time.
Yeah, he got the Illuminati working on that too. But I believe, somehow, Yukio wants to help Satan -his own way- (he's still stubborn and he already claimed "the Order and the Illuminati are both bad" which in my mind sounded like "You two are the same. So I'm not gonna side with any of you."). So now it's Yukio AND Satan working together.
Does Yukio really want to help Satan annihilate Assiah? I think not. But he may want to trick Satan into believing that (and I think Yukio's aware he's gonna 'cause casualties, but) so he'll play along with Satan's plan for a while. And here's where Rin comes into play.
And here's where I start analysing chapter 95. Back to Yukio's plan: I'm sure the choice to have the shooting happen during the live broadcast was calculated. Yukio knew he was gonna be arrested if he was seen holding the gun. But he knew that Shura would've obviously tried to defend him. And here's where it gets tricky. If Yukio was proved innocent in a question of hours, he would've been released and... case closed. But, Yukio plans to "help" Satan and if Satan somehow needs Rin "to lay claim on Assiah" than, he gotta think of a way to get to him. I'm gonna be honest, this next part is not as easy to explain and I'm not quite sure about it myself. It looks too (way too) far-fetched, I know, but I got something like a reason for this and I'll tell you in the end.
So, let's say Yukio needs a plan to lure Rin. One that will force him to even leave the Order with no chance to get back. And, technically, if Rin's gonna complete his "Yukio's rescue" quest, there'll surely be no coming back for him. His "betrayal" will result into experiments, or even the infamous execution. Maybe that's the point where Yukio's trying to get Rin to. Let's skip this for now.
Yukio planned for the shooting to be broadcasted. He knew Rin would see it/been informed about it. And he knew that Rin would've come to rescue him. But, as I said above, if Yukio was proved innocent, he would've been freed in a question of hours. Nothing biggy. And... that's why Yukio needed a more effective plan. Why not showcase his Satan-shaped eyes and have him confined 'cause of them? Again, the eyes -conveniently- change shape at quite the right time.
Anyway, why do Yukio's eyes -apparently- randomly change shape? I thought of this: what if Yukio asked Satan to do so/they can somehow communicate, like, telepathically now and Satan takes over Yukio's eyes at "command"?
This aside, screw the shooter matter, Yukio can't escape from this. Shura tells Rin about Yukio and... in the last panel of chapter 95 we get Yukio's "I was expecting you to show up" look. Which I'm gonna translate into "I was waiting for you to show up." 'Cause, really, Yukio knew Rin would do it. And that's why I think he set him up on purpose.
So, after all this nonsense, I'm gonna even place a short prediction based on this crappy theory: Kato-sama loves plot twists. We're all expecting Yukio to stay silent, to yell at Rin, Rin to yell at him... but I think we're all expecting Yukio to NOT follow Rin out of that room. Believe it or not, I have a feeling that if there's some big plan behind these last 2 chapters and will be revealed only later, for the next few pages we'll get some unpredictable event, like: Yukio quietly accepting Rin's help and actually letting him rescue him. I think it'd fit Kato-sama's style. We'd be left like: for real?! But the truth will be revealed only later. Maybe even by the end of chapter 96. And I think that would be quite one hella cliffhanger...
One last thing, about Satan's plan and Yukio needing to hand Rin to Satan for something. Why would Yukio trick Mephisto and have him actually shot? We know that Yukio knows about the Artificial Gehenna Gate. In chapter 42, Shura hands him a report with a pic of the Gate. I'm not sure (but I guess yes) if Yukio knows about the barrier that Mephisto put around it too. So, the moment Yukio aimed his gun at Mephisto I'm guessing he knew that by weakening him, the barrier would've collapsed. So the answer is: Satan -can prolly- come out of THAT Gate and "walk" into Assiah (even if not in "physical" form). Something like in the anime, I guess. So he needed for the Gate to open and the barrier was a problem.
AND Satan needs Rin. The only thing I could think of is making a connection to the anime again. Grandpa Egin states that he could "save" Rin by having him lose his demonic powers by destroying Gehenna. So Yukio, at first, tolerates him (Grandpa Egin) using Rin as a "sacrifice" to open the Gate. He than can't stand watching Rin "suffer" anymore and offers to take his place. But, at first, he was somehow accepting to let Rin be used for the sake of the plan.
To make things even more complicated, Yukio (in the manga) could even be faking to be using Rin as a "sacrifice" to offer to Satan but will reveal it was just a trick. Like, when he tricked Hachirotaro into thinking he actually shot Rin with real bullets. Why? Really, 'cause I hope, deep inside, that Yukio somehow still cares for Rin. I hope...
To make a last connection with the anime. Grandpa Egin gave Yukio the role of Paladin. That's also why I think Satan may offer Yukio "power" in exchange of his help. But, Yukio, in the end, will never be actually planning to get help from Satan. He will just be using him for the sake of some bigger and more complex plan and... that's quite all. I'm done! Sorry for this long ass post again. I thought all this at 3 am last night so... I guess I better sleep at that time next night.