The second part of that restriction won't fly. I should've been a bit broader "no solo every X" to include things like switching out and the like. I'm even less likely to remember to switch out of a bunch of random moves than I am to remember to fight a specific type of Pokemon.
Jimera0 Take Subluminal the Snivy. Subluminal the Snivy wants to move faster than light itself. However, it can not. As such, it may not use any light-based moves, and it must swich out against pokemon that use them (Confuse Ray, Dragon Pulse, Dragon Rage, DragonBreath, Earth Power, Energy Ball, Flash, Flash Cannon, Focus Blast, Glare, Heal Pulse, Hyper Beam, Light Screen, Mean Look, Mirror Coat, Moonlight, Morning Sun, SolarBeam, Sunny Day, Synthesis). Because it wants to be so fast, ideally it would have a + speed nature and 31 speed IVs (these are suggestions, not rules, because there is about a .5% chance of a random Snivy having such requirements met).
It also has heard Team Rocket's motto of "Team Rock blasts off at the speed of light." As such, it wants to help Team Rocket, so they can spread their superluminal technique. Since it can't go to Kanto or Johto and join Team Rocket there, it must try to obstruct Team Rocket's foes. And since Team Rocket and Team Plasma are both aiming for global domination, it figures the two of them must be butting heads (Metaphorically, that is. I'll save a challenge based off of some idiom for later). As such, from when the first Team Plasma member mentions their goal of global domination (or when a pokemon uses Mind Reader on a Team Plasma member's pokemon as well, if you are fine with that), it must battle against as many Team Plasma members as possible (solos, scenarios where it can't fight, scenarios where it can fight, but can't win, et cetera exempt), and perform as well as it can in those battles.
It also knows that no pokemon is faster than light. It, therefore, does not want a pokemon to be faster than it, for that would mean it is not faster than light by a long shot. As such, it may not battle against a pokemon faster than it (factoring in natures, speed stat, level, EVs, IVs, and stat stages, but not priority or items).
If you want to, you can breed Subluminal to give it perfect IVs, an ideal nature, and/or egg moves. However, doing so is not required.
Alright, you kinda made it worse. All this stuff is falls under the last category pretty much. The problem are challenges that have a condition I have to notice in order to act on, and these are conditions that aren't always present so unless I'm paying attention I'm going to totally miss it. Also, a lot of your "light based moves" don't seem light based to me. This wouldn't be an issue if they were just moves I had to remember not to learn, but since I need to be able to recognize and remember every time they're used in battle I'm just never going to remember. Finally, the fact that you're making me solo Plasma grunts only AFTER I've noticed them saying something about world domination is bad too because I'm going to get into the habit of NOT having to solo them and then half way through the play through I'll have to start remembering. Additionally, it requires me to play close attention to every grunts dialogue and remember when reading that dialogue that I'm supposed to be looking out for mentions of world domination. Finally, the "cannot battle faster Pokemon rule" is the worst case of "You cannot battle X" rule because I'll have to be looking out for it in almost every battle.
In short, I can't accept this challenge in its current form because it's exactly what I was attempting to warn against with my last guideline. Maybe if you change it so I don't have to remember to act on all these situational things you can save it, but as it is this challenge is basically my worst nightmare. I'll only remember to do any of your restrictions about half the time as it is.