I beat him twice in a row within 7 minutes each time doing this with Rikku alone.

Rikku = 17260 hp, 170 strength, with Haste and Protect on, only member in the party. Tidus and Wakka are dead.

Rikku Quick Hit, Shinryu counters, 4000 damage.
Rikku Quick Hit again, Shinryu counters, 4000 damage.
Rikku Curaga, Shinryu either attacks or uses Shining. Heal after turn.
Repeat. Keep HP up, and attack til he dies.