If this version of the Mandarin is more dependent on the rings, and not *also* a top-tier martial artist, and scientist, and mystic, and businessman, and possibly really good at celebrity show cooking and a master of the fandango, Shang might be able to use the same sort of evasive techniques a movie martial artist would use against a nut with a gun. The rings are, more or less, just a really amazing set of guns, shooting fire, ice, lasers, lightning, spinny vortexes, hypno-beams, etc.
It would make for something quite different than the usual martial arts movie climactic end fight, with everyone kung fu fighting, having Shang be the martial arts master, using more ground 'realistic' (ish) fighting techniques and the Mandarin being all pew pew, lazors, over-relying on his rings to win the fight, and the end message being something, something Shang and discipline and training and skill and heart overcomes alien jewelry and sheer arrogance.
It could be super-cool, with lots of different ring effects coming out, and Shang having to evade or deal with whatever complications arise. Mandarin negates light with the darkforce ring, and Shang demonstrates the skill to blind-fight, for instance. Mandarin creates a paralyzing fog of gas with the matter rearranger ring (which could do all sorts of crazy ****, but paralyzing 'nerve gas' seems to be his favorite), Shang holds his breath and seizes some ornamental war fans off the wall and blows the cloud away while fighting with them. Mandarin creates a slippery coating of ice on the floor with the ice ring, and Shang leaps atop a nearby table and 'walks' along the walls and tops of statues and whatever in the room, avoiding the slippery floor and kicking the Mandarin on the way by. Showy over the top stuff like that.
Or it could end like every other martial arts movie, with two dudes punching and kicking each other, which would be fine too. Gotta respect the classics.