How do you get the Season 2 Reward - Platinum Solo?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Platinum in the 2012 ranked season in Solo/Duo.”
Is the Season 2 Reward - Platinum Solo still available?
No. The Season 2 Reward - Platinum Solo was a ranked reward: to get it you had to reach Platinum in Solo/Duo during Season 2 (2012). Riot does not give out past ranked rewards again, so it cannot be earned anymore.
