What are the Red Stars for in Sonic 4: Episode 2?
Unlike the other Sonic games, in Episode 2, the Red Star Rings are mere collectibles. Collecting all of them don't unlock any special features/stage in the game, you'll only get an achievement after you collect them all and beat the boss in Death Egg mk.II Zone Act 1.
Source
One Red Ring is hidden per act, and an achievement is unlocked after collecting them all.
http://sonic.wikia.com/wiki/Sonic_the_Hedgehog_4:_Episode_II