Alright, I realized that I wasn't going to get a brilliant explanation of the Ranking System in the story, not without making it brutally obvious narration. So I'm going to just explain it here.

First things first, it is two separate systems that relate to each other.

There is the Pokemon Ranking System, and then the Trainer Ranking System. They are separate.

A Pokemon's ranking is not about strength or power, it is about danger. How dangerous can raising it be to the trainer or those around them? That's all it means. Incidentally, this often leads to more powerful pokemon having higher ratings, simply because they are inherently more dangerous.

The Trainer's Ranking is a mix of knowledge and strength. It is half about knowing how to take care of your pokemon and making sure having them with you is safe and that they are taken care of. The other half is built off of how strong you are as a Trainer. Hence, you can increase your rating as a Trainer through knowledge OR by getting stronger.

You can increase your ranking in three different ways. Every two gyms badges, your Ranking will be increased automatically by one. That's one way you can increase your ranking through strength.

The other two methods are through getting an Assessment. With an assessment, you have two options. You can go for a Strength or Knowledge assessment.

A Strength assessment involves bringing in an Ace Ranked Trainer and having you battle them. Depending on how you did, your Ranking might increase, or even decrease. It'll change to what it reflects, instead of the Gym Badge's automatic increase.

The Knowledge assessment involves a test of your knowledge about your pokemon and others. You also get examined to see how you interact with your team and how healthy they are, as well as how obedient. Your ranking then increases or decreases to reflect this.

Now, for the rankings themselves, they go like this:

E-Rank - Really Bad Beginning Trainers / Very Safe Pokemon

D-Rank - Mediocre Beginning Trainers / Relatively Safe Pokemon

C-Rank - Good Beginning Trainers / Dangerous under circumstances Pokemon

B-Rank - Best Beginners or slightly Experienced Trainers / Can be dangerous if mistreated Pokemon

A-Rank - Experienced Trainers / Dangerous if mishandled Pokemon

Ace Rank - Very Experienced Trainers / Dangerous Pokemon

Elite Rank - Most Experienced Trainers / Very Dangerous Pokemon

Champion Rank - The Best Trainers / Legendaries

The only ways to get Ace through Champion ranks is to either test knowledgable enough about pokemon, which pretty much only dedicated scientists or professors can do, or you have to beat someone of that rank in an official match, showing that your team is of that strength.

I've also decided on a couple other methods of advancing beyond A-Rank. If you get into the Top Eight of the League Tournament, you can advance one rank automatically, up to Ace Rank. And if you Win the Tournament as an Ace Rank, then you can advance to an Elite Rank. To become a Champion Rank you must defeat the Elite Four or beat a Champion Rank. If you defeat the current Region Champion then you can become the Region Champion, but otherwise you are just at the rank.

I hope this helps with understanding the story in the future!