Defeating Arachne
To defeat Arachne (the first Boss), find the glowing pedal on the ground. Go to it and press Circle. When Arachne gets close, press Circle to throw the 'egg'. She will leave her stance to care for her egg. Follow and attack her. Do this as many times as needed (usually three or four) and she will disappear. Go through the new door to finish the level.
Faster Boat
To make the Jammy Dodger boat go faster, either hold X and keep going straight, or continue moving while moving the Left Analog-stick Left and Right then straightening it out.