This may be a bit of a stretch, but I really want to say this is
Organization XIII from Kingdom Hearts
Finish of bronze
Laxaeus, The Taciturn Stalwart. I have no idea why though.
Finish of gold
Xemnas? Since he's the boss, he's the gold medal, the number one. I'm really stretching here.
Uncurse my bluff
This refers to Luxord, also known as the Gambler of Fate. Bluffing is related to gambling.
The way will be told
Maybe Larxene? She tells Sora about how he forgot Namine, which leads him deeper into Castle Oblivion.
In fiction and fact
This refers to Zexion, the Cloaked Schemer, known for his powers of illusion.
At the edge of the grave
Axel? He sort of dies helping Sora rescue Kairi, except he's not quite dead.
I'll fit in a tux
Demyx, possibly. Also known as The Melodious Nocturne
If I see where you pave
I believe this is referring to Xigbar, the Freeshooter. If you get in his line of sight (or if he sees where you step/pave), he'll shoot you with his sniper rifle.
I'm a dragon part
I believe this is referring to Xigbar, also known as the the Whirlwind Lancer. He controls Dragoons
A circus split up
Saix, The Luna Diviner
I'm at the term's start
Marluxia, also known as The Graceful Assassin. He shows Sora into Castle Oblivion, hence the first Organization member ever introduced.
To pass, sum it up!
This may be a stretch, but is this Vexen, The Chilly Academic?
I'm pretty sure you are referring to Roxas here. At the beginning of the game, he doesn't know who he truly is. Even later, when he merges with Sora, everyone in the Organization refers to him as Roxas, confusing Sora.
There are thirteen members of the Organization that makes up their name