Yes I unlocked my 4 and 6 Billion achievements after trying the runs without restarting. That seems to be the case, also make sure you keep an eye on the small dot in your stomach,that is your hit marker, if it is hit you take damage, any other part of you can be hit. On a final note if you turn off continues and set your lives and bombs to 5 you can get every achievement, whether this is old news or not here it is anyway.
Arcade 100%: 34//Latest: Sonic 4: Episode 1//Current: Castlevania HD
Retail 100%: 16//Latest: Borderlands//Current: Sonic Unleashed