I am that which follows Omega...
Shinryu is a superboss in Dawn of Souls and succeeding editions of the original Final Fantasy. He is arguably the hardest boss in the Dawn of Souls release, along with Omega, but Chronodia takes its place in versions thereafter. He is encountered on Floor B20, the final floor of the Lifespring Grotto, and either he or Omega must be defeated to complete and leave the dungeon.
Shinryu uses attacks that inflict large amounts of damage to all party members. Although he can use Thunderbolt, Ice Storm, and Tidal Wave, the biggest threat is his Flare. With each casting, Flare can either leave the party close to death, KO a few and leave the rest on the verge of defeat, or destroy them outright if the player is ill-prepared. Shinryu's physical attack can inflict heavy damage as well.
The speed at which Shinryu can cleave through a party makes this battle more about all-out power than anything else (instead of the endurance battle Omega ends up being).
It is best to be at level 70 or above (though lower-level wins are still possible). The successive castings of Flare are dangerous, even to high-leveled parties. Victory is likely if Shinryu does not wipe the party out in the first few turns, because he only has 35,000 HP and is susceptible to high-powered physical onslaughts using the usual strategy of Haste/Temper.
Shinryu is the Japanese on'yomi name for Shénlóng, literally "god/divine dragon", an important ancient dragon in Chinese mythology. It is said to preside over storms and rain, and can bring disastrous drought, thunderstorms and general bad weather if it feels neglected and/or angered.
A notable difference between common Chinese dragons and a Shenlong/Shinryu is their fingers; the latter have five on each hand as opposed to four, and they are said to share the same green-blue-ish color as another mythological dragon, the Qinglong/Seiryu (lit. Azure/Blue Dragon). The Final Fantasy interpretation has four fingers on each hand.