Amy plays a part in the story, getting into Prison Island somehow, breaking Sonic out of his cell, running from cops, and getting caught by Eggman, but all that stuff happens offscreen. We don't get to play any of that.
But what if we did?
What if they played like Amy's stages in SA1, where you have to run from a persistent, indestructible robot until you grab the balloon at the end? Here's what I'm thinking...
Okay, so, the story still starts with Sonic breaking out of a helicopter midair, racing through Stage 1: City Escape, fighting F-6t BIG FOOT, meeting Shadow, and then being recaptured by GUN. Then Knuckles still meets Rouge in the Desert Area and hunting down emerald shards in Stage 2: Wild Canyon...
But then, before we cut to Tails flying his Tornado over the ocean, we first cut to Amy, buying groceries in Station Square, where she hears a newsboy shouting, "EXTRA EXTRA! Read all about it! Sonic the Hedgehog arrested and jailed for bank robbery!"
Amy gets fire in her eyes and says, "Not MY Sonic!" She drops her groceries and runs towards the docks.
Now she's on an aircraft carrier, and a GUN security guard in a mech is yelling at her, "Stop immediately! This is a secure facility and strictly off-limits!"
She stares daggers at him and says, "NOBODY keeps me from my Sonic!" Then she starts running through...
Stage 3: Armored Marina. It looks similar to Metal Harbor and Weapons Bed, with their docks and pulleys and aircraft carriers, but with the security guard in the mech suit chasing after you, and there being a big balloon with a handle at the end.
Then we see Tails flying over the ocean in his Tornado and finding Amy being menaced by Eggman. Tails fights Eggman, then tells Amy to stay put while he goes through what is now moved up to Stage 4: Prison Lane. But then, after Tails gets to the prison core, we cut back to Amy infiltrating...
Stage 5: Restricted Zone, that looks similar to Prison Lane and Iron Gate, with their corridors, elevators, and locked gates, that Amy can break with her Piko-Piko Hammer. You have to get past the GUN warden in his mech, and get the key to Sonic's cell, then grab the balloon at the end.
So then Amy teases Sonic for a bit, then uses the key to open his cell. Then he runs through Stage 6: Metal Harbor, fights Shadow, and runs through Stage 7: Green Forest. Knuckles goes through Stage 8: Pumpkin Hill. Eggman broadcasts his threat and blows up the moon. Then Sonic, Tails and Amy get chased by the police. Sonic and Tails run off and don't wait for Amy, forcing her to make her way through...
Stage 9: Rash Road, which resembles Mission Street and Radical Highway, with their unsafe roads, barricades, cop cars, pulleys, and rockets. You have to run from a mechanical paddy wagon and reach the balloon at the end, again.
Then Tails goes through Stage 10: Mission Street and Knuckles goes through Stage 11: Aquatic Mine, then comes out of a manhole in front of Tails and Amy, and Tails goes through Stage 12: Route 101 and drops in on the president with Sonic. Then Sonic, Tails, Knuckles and Amy go to the Desert Area and discuss getting to the Space Colony ARK, and Tails says he'll find the entrance to Eggman's base. But this time, Amy says she'll distract the guard and goes into...
Stage 13: Quicksand Moat. It resembles Sand Ocean and Hidden Base, with its stone blocks, stone doors, and hieroglyphics, but you're being chased by Eggman's security robot. As usual you have to grab the balloon at the end.
So then Tails goes through Stage 14: Hidden Base, Sonic goes through Stage 15: Pyramid Cave, Knuckles goes through Stage 16: Death Chamber and fights King Boom Boo, and Sonic fights the Egg Golem. Then the four animals take a rocket to the Space Colony ARK and the Master Emerald shards fall out and Knuckles jumps ship. Then Sonic and Tails leave Amy behind again and Tails goes through Stage 17: Eternal Engine. Amy has to fend for herself and stumbles upon a larger and stronger Artificial Chaos that chases her into...
Stage 18: Panic Passage, which resembles Lost Colony, Eternal Engine, and Crazy Gadget, with their space age looking rooms and hallways, and rails through space, and zero gravity sections. You're running away from the bigger Artificial Chaos and have to grab that balloon one last time.
Then Amy has to fight the big Artificial Chaos in a boss fight.
Then Amy is exhausted and distracted, and Eggman captures her and holds her for ransom. Knuckles goes through Stage 19: Meteor Herd and fights Rouge, Sonic goes through Stage 20: Crazy Gadget, Tails fights Eggman again, and Sonic goes through Stage 21: Final Rush. Then credits roll.
And no, Amy does not have a part in Cannon's Core. Sorry Amy.