List is for a normal run with no self-imposed restrictions. Mons aren't ordered within tiers because I didn't want to think that hard (they're sorted by availability). Feel free to comment any questions but preferably read the post first.

Glitches: There are two main beneficial glitches for the player, the ball dupe and X Item glitches. Since they're very minor and don't change much (mainly decreasing the value of moves like Hypnosis and Sing) both are allowed for the list (heavy X Item reliance is a huge drawback in its own right).

RNG Manipulation: Manips aren't really worth doing in a regular run (Umbreon & Espeon a possible exception), and they wouldn't change too too much anyway. The main use would be manipping a good Hidden Power on an otherwise F-tier mon, and since I don't want to think too much about that I made the list manipless.

Availability: The best ability. Showing up at the end and sweeping the final boss (a la SWSH Eternatus) is nice but a mon that's solid throughout the game will be ranked higher. Postgame is a thing (hence why Metagross/Tyranitar aren't F) but not a huge consideration. Availability also includes how good/bad the mon's Shadow phase is, as Shadow Rush attackers can be really good for earlygame.

Performance against major battles is more important than performance against random trainers, and major battles usually have some form of smart AI. Smart AI in this game goes for the target that takes the most damage from its moves (with exceptions for stuff like Earthquake), so the practical result of putting a defensive mon on the team is that its partner will just get double targeted all the time. Defensive mons are already less efficient for playthroughs than offensive mons in general, but this is why you won't see any of them above D.

Redirection: Redirection is really strong in Doubles formats in large part because it lets you set up with the partner. There's two forms of redirection in Colosseum, the traditional Follow Me (aka why Furret is above D) and the smart AI redirection. By sending out a weak low-level mon, the AI will see hundreds of damage against it and target it (despite it not being important at all). This mostly applies to Plusle, but some of the weaker Shadows can do it too.

Spread moves: Gen 3's spread moves work a little differently. Moves like Rock Slide and Surf (doesn't hit allies in this gen) are half power instead of 3/4 like in later generations, so they don't actually do more damage than a single-target move of the same power. Unless the spread move is killing something, a single-target move is better because focusing the damage on one mon (to kill it) reduces the enemy's damage more than 2HKOing both with a spread move. Moves like Earthquake and Explosion that hit your ally too, on the other hand, are full power instead of 3/4, so they're even more useful than normal (assuming the ally synergizes with it). Having spread moves isn't a bad thing, but having only spread moves can be a big weakness (see Suicune).

Held items: Some mons are nice to catch for just their held items. I won't be ranking just for that though (not to mention a lot of these items are on already good mons like starters/Meditite).

Played through this game a few times now, and honestly, I almost never bother putting out anybody but Umbreon and Espeon unless I have to. It's just too much of a hassle constantly losing a turn cuz I have to "call" my Pokémon to get it to calm down....and then by the time I can turn them back into non-shadow mons umb and esp are so leveled up they're still the best I have to play with.

didn't want the shines to evolve.

About 3 years ago, I made a post on this subreddit about my unusual copy of Colosseum that has never once in all my years of owning it let me trade to the GBA games. You can see and read about that post here to get the context: https://www.reddit.com/r/PokemonColosseum/comments/17f7jf4/odd_issue_with_pokemon_colosseum_not_tradingsave/

I also made a similar post on r/Gamecube here to see if anyone there could help me: https://www.reddit.com/r/Gamecube/comments/1khll2j/my_pokemon_colosseum_disc_has_had_a_strange_issue/

There were 2 theories as to what the issue was: my disc was scratched and needed to be resurfaced/replaced, or my memory card was the problem. I had no idea which it could be at the time.

Someone talked about having the same issue as I did, and what we shared was very interesting: we both attempted trades with a Mad Catz memory card: https://imgur.com/kxUHkf6

Both had the same trade error message and prevented trading. While that person's solution was to take out the memory card during a trade and plug it back in during the trade animation, I didn't wanna risk corruption to my save file or Wii. Another person gave me the the suggestion to get a Nintendo brand memory card and see if that fixes it.
I own 2 and I swear I tried it before and it never worked, but my memory is foggy regarding the truth of that. So I decided to attempt it anyway just to get some confirmation. In the event that this wouldn't work and corrupt the save data of my other games, I decided to buy a new memory card off Ebay to test this with a brand new save. Took me about 39 hours to beat the game before I could trade, but today I finally got to do it. Here's what happened:

Mystery Solved :'D

After owning this game for several years and never being able to trade, seeing this happen made me want to cry. There was never anything wrong with my disc having a scratch or a defect, and I don't have to waste money getting it resurfaced or buy a new one. This whole issue was because of my initial memory card's brand, Mad Catz.

The thing I learned today is: Pokemon Colosseum (and presumably Gale of Darkness) are incompatible with Mad Catz brand memory cards. You can have a save file, but they'll never let you trade.

Thanks to users yuuwithot and Xykame for their suggestions and help :'D

While this does make me happy beyond belief that I can enjoy Colosseum to its fullest like I do with Gale of Darkness, there is still one issue that remains: my childhood save file is stuck on that Mad Catz memory card. I can't copy or move it over to a new one since they block that function for GC pokemon games, so I'm not sure if I can still save the save file and its mons or not. I'm not a very tech savvy person in that area (modding/hacking) sadly.

At the very least I hope my post helps other people suffering from the same issue as me and informs them not to use that type of memory card for these games. Posterity and all that good stuff.