Arrow keys move character around
A - attack/kick
S - shield/duck into shell
S + hold D - dash charge
S + release D after holding it - dash
X - fruit bomb
In case you end up seeing stars, quickly press LEFT+DOWN+RIGHT+UP over and over until you've awoken yourself from the daze.
Be careful when swimming, lots of momentum; Watch out for the spikey villains!
Oh! One more thing! Those little fruit bombs pack quite a mighty punch! They'll flip you over and flop your shell right on its back without any qualms of tipping you back over. Move side to side repeatedly to gain build momentum in flipping back over—but not too quickly! If you're moving side to side without following the rhythm, your efforts will be in vain.