His attacks resemble Tidus's Overdrives in Final Fantasy X (albeit with different names), and deal heavy damage. He will cycle through them, throwing in regular attacks in-between. Shuyin's agility is high and so is his evasion. Terror of Zanarkand will probably K.O. any character, but he seems to favor Yuna, and if she is alive he'll target her above the others.
Yuna should not be the designated healer. It is best to heal whoever gets hit by Shuyin while having the other two party members attack full force. The best strategy is to use Light Curtain on the party for Protect. It would also be wise to steal the extremely rare Hero Drink item from Shuyin.
"Their Resting Place" plays during the battle with Shuyin. The theme includes a dark reprise of the melody of "1000 Words," the game's vocal theme, which in the context of the story Shuyin's lover Lenne wrote as her last song to him, but which he never heard.