Easiest way i guess....

Four coral rings

Have one character hold masamune and cast Hastaga as soon as the battle starts. Shinryu will use Tidal wave which you absorb. Then unleash Rapid fire + 2-swords, Flare + doublecast, and Quick + Throw (Fuma shurikens) He won't last a couple of turns

Alternetively you could go all out defense. It's possible to absorb/evade/block every single attack shinryu has

Physical attack - Blink/twin
Poisen breath - Bonemail/ Resist poisen
Blizzard - Resist ice/Dragon shield/Ice shield
Lightening - Resist thunder/Dragon shield
Atomic ray - Resist fire/Dragon shield/Fire ring/flame shield
Roullette - Bonemail/Life shield
Akumas eye - Ribbon
Mealstrom - Dragon kiss
Level 2 old - dont be a level multiple of 2 :P
Level 3 Flare - Dont be a level multiple of 3 :P
Mighty gaurd - Harmless

He cant touch you if you set that up to one character. Bit of a mission gettin that on your entire party, but three characters setting up one character will make you invincible