How do you unlock more Summoner Icons?
The Summoner Icon popup says that you can unlock special icons via accomplishing achievements in the game.
As far as I can tell, I've never unlocked a new Summoner Icon, or at least have never received a notification that I have. Is there a known list of the achievements that you need to get in order to unlock new icons, like getting to level 30 (which I'm not yet), getting X amount of Kills/Assists/etc.? What icons can I unlock?
I don't think that was ever implemented. I have played probably like 1,000 games and I have never unlocked an icon to my knowledge.
I've quit LoL an year ago but i was sure that at that time, there were no unlockable icons. There were rumors that early beta testers had particular icons but it turned out to be a bogus. I don't know if anything changed recently.
I tried to track down the red post in which I saw this, but I can't so I'll make this a comment instead of an answer. Achievements were put on temporary hold due to potentially creating undesirable behavior, such as KSing or intentionally slowing your team's victory, in order to complete an achievement. Even achievements for desirable behavior can result in someone abandoning their own lane, rushing over to tackle an objective that their teammate can take care of alone.
AS someone who started in beta I never got a new icon... got 10wins in a row, and stats i was proud of but nothing ever happened
The new summoner icons are to be unlocked via achievements. However, achievements haven't yet been released in LOL (You'll find the 'not yet accessible' tab in your summoner profile). There have been quite a bit of rumors lately on what the achievements would be, but I still haven't found anything serious on the subject.
Conclusion : Wait and See
Indeed. I actually never even read that paragraph when I chose my icon. I think I was too busy looking at all the pretty icons to read anything. But when I read your question I was very curious to know how to get new icons. What a bummer.
So it will only cost you actual money.... What kind of achievement is that?