You can unlock up to four boosts by connecting Sonic Boom: Rise of Lyric to the 3DS game Sonic Boom: Shattered Crystal from the main menu.

Boost	How to unlock
Increases maximum Rings by a huge amount and rings will slowly regenerate	Defeat Lyric (in Shattered Crystal)
Increases maximum Rings by a large amount	Beat Metal Sonic in a race (in Shattered Crystal)
Increases maximum Rings by a medium amount	Beat Sticks in a race (in Shattered Crystal)
Increases maximum Rings by a small amount	Use the Nintendo 3DS Connect Feature.