that's not it. I'll give you another hint: it doesn't have to do with mechanics.

Singed is the only one from beta?

i'll give you another hint: it has to do with events.

This is triicky
Amumu has vancouver skin from 2010
Kat has world cup skin
Kat has haloween skin
Vlad has nosferatu
Siged has riot

is it Kat because she has 2 event skins?

those are the wrong kind of events as those are skins. :3

Katarina again, was the only one not chosen in the 2010 Ionia Vs Noxus rematch

this^ your turn

Can I have a go?
Twitch
Talon
Sona
Rengar
Amumu
Olaf
Nunu
Poppy
Vayne
Vi

I'm pretty sure its bwares turn...

But a guess to yours would include
Amumu is the only champion from the collector's edition for LoL
Sona is the only one who can't speak
Nunu is the only one that has two seperate beings making up the champion
Talon is the only Noxian
Vi is the only one from piltover
Amumu is the only yordle
or that twitch is the only one from zaun.
I think I exhausted all the easy ones...