Final Rush is the final stage of the Hero Story of Sonic Adventure 2. It takes place on the ARK in order for Sonic to reach the Eclipse Cannon. It is the equivalent to Shadow's last stage Final Chase and features many grind rails suspended below the ARK's underside.
After Sonic was blasted off in a capsule that was going to explode in minutes by Dr. Eggman, Sonic uses his fake Chaos Emerald that Tails had given him to use Chaos Control. He then warps on the ARK in front of Knuckles who just finished looking for the Master Emerald. Sonic tells Knuckles that he is going to continue with his mission of putting the fake Chaos Emerald in the Core. He then meets Shadow, who is suprised that Sonic activated the Chaos Control using an emerald that's fake. They then face each other and Sonic defeats Shadow. Tails and Amy are grieving over Sonic's "death" when Sonic contacts them and Eggman takes the real Chaos Emerald. They look outside and watch Sonic destroy the Eclipse Cannon.
Sonic's Mystic Melody is found here.