Sonic's Secrets: Arrow Flash.

At the options menu (see right), change the "Arrow Flash" setting from Stock to Charge.

Now wait for, and watch, the the story demo. When the gameplay demo begins press Start.

Now when you start a game if you press the C button for 5 seconds, when you release the button you will be invincible for 10 minutes. 

NOTE: only works whilst you are in 'Mecha' mode.