Sorry for replying to a year old comment, but from looking at the achievements section, they are:
The palmtree one is the Quick Run, which is completing EHZ1 under 35 seconds,
The Chemical Plant one is 100% Chemical Free, which is completing CPZ2 without going underwater,
The chaos emerald one is Early Bird Special, when you get all 7 chaos emeralds before CPZ,
Super Sonic is Superstar, when you complete any act as Super Sonic (btw why did they use the S1 super sonic),
The jackpot one is Hit it big, when you get a jackpot on the CNZ slot machines,
Eggman in his flying thing is Bop Non-stop, which is self explanatory,
The ring is Perfectionist, when you get a perfect bonus by collecting every ring in an act,
The dino badnik is A Secret Revealed, which is also self explanatory,
The 2P VS one is Head 2 Head, which is winning a 2P Versus race against a friend,
The MPZ things is Metropolis Master, when you complete any MPZ act without getting hurt (which I'm sure is pretty much impossible),
Just ordinary Eggman is Scrambled Egg, which is defeating the Boss Attack mode in under 7 minutes,
And finally, the signpost is Beat the Clock, which is completing the Time Attack mode in less than 45 minutes.
Hope this answered your question Smoke.

what does each achievement mean? hmm.