I cleared Shinryu on launch weekend, in a party with people in 290 or lower gear. Mostly lower, because the only option to get anything higher was to farm Ala Mhigo, and most of us were rushing to get the story done before spoilers popped up. It only took us three tries, and the first wipe was from Tidal Wave.

If you're still struggling now, all anyone can really say is "learn the mechanics". Shinryu is a fairly busy fight, but it's not hard.