Actually a tooltip does say so in Generations that for S-rank, you have to do an A-rank without dying, and that's it.
And yeah, one thing I missed that Generations didn't had an epic Last Boss Second-Phase theme, that was the norm ever since '06.
Actually, maybe it is an era change again, if you notice: The three "Genesis era" games, Sonic 1, 2, 3&Knuckles all had unique but kinda "normal" Final Boss Music. The "Dreamcast era" games, Adventure 1, 2 and Heroes, all had rock-ish themes for the Final Boss. And then the three "Modern era" games, Sonic '06, Unleashed and Colors all had the epic orchestrated version of their main themes as the Final Boss Second-Phase theme. Interesting coincidence imo.