Completing the Final Zone
When running up the robot's arm you must stop and crouch at the low point between the forearm and the shoulder. This will prevent you from flying off once he waves his arm.

Extra Zone
Successfully complete Sonic's and Blaze's story line with all seven Chaos Emeralds to unlock Extra Zone at the character selection screen, where you play as Super Sonic and Super Blaze.

Play as Blaze
Defeat the first Boss to unlock Blaze.

Remain in air longer with Blaze
To stay in flight longer while playing as Blaze the cat, instead of holding R, rapidly tap R. This should increase your time of flight in the air by a lot.

Sound Test
Successfully complete the game to unlock the Sound Test option.

Time Attack mode
Successfully complete the game to unlock Time Attack mode.