During one month of every year, something appears over the skies of Never Lake. A small planet, conveniently known as "Little Planet", which contains seven Time Stones said to be able to control the passage of time in some way. This of course catches the attention of Dr. Eggman (a.k.a Robotnik) and ever the opportunist, he chains the planet down to a nearby mountain (now sporting his ugly mug) when it next appears. By controlling the flow of time on the island, he visits the past and places his machinery around the place so that he can turn a once peaceful, tranquil future into a metallic empire in only an instant.
Where's Sonic in all this? As indicated by the game's snazzy anime intro, he's hurtling across Never Lake, but it's too late, as he's shocked to find the planet covered in Eggman's diabolical machinery! Without hesitation, he climbs the mighty chain and heads on up to investigate. Little does he know that at the time, Amy Rose, his biggest fan, was lead to the planet by a tarot card reading that told of a destined meeting with her hero. Eggman, however, has an ace up his sleeve and the young girl becomes the perfect target. A new enemy makes himself known; Metal Sonic, designed to match Sonic's every move, and even be able to reach his same impressive speeds. To add to Sonic's problems, this metallic duplicate kidnaps Amy right in front of him and flees. Now he's got to save the world and get the girl, despite not really wanting her in the first place.
Strangely, the US manual at the time referred to Amy Rose as "Princess Sally". For those that don't know, Princess Sally is a character that features heavily in the US Archie Sonic comic and old "SatAM" cartoon show that began around that time. She has never appeared in any game, except for a brief cameo in Sonic Spinball, which was based on that alternate Sonic universe anyway. This was a poor attempt to tie the two in, so that kids that are too intuitive won't start asking questions, but it fails to explain the fact that Amy in the game, quite clearly, looks absolutely nothing like Sally in the comics and cartoons. Having said that though, I do seem to recall seeing some official American art where Sally was pink, instead of her usual brown colour. Interesting. Also, in the English manual for the PC port, "Mobius" is clearly named as Sonic's planet, which is also taken from the storylines of a variety of Sonic cartoons and comics from the 90's. However, the name of the home planet is never really officially stated in any other game or game manual, English or Japanese, until the post-Sonic Adventure era where it's referred to as Earth, once or twice. This version of the story also seems to contradict the one explained above by implying that Sonic and Amy were already friends as they approached the Little Planet, together.