For the fight with Zenos, all I can say is that we learned his secret when we fought Fordola, but I can't say how we exploited it. However, for Shinryu we can say 2 things for certain: 1) Omega did significant damage to Shinryu prior to us fighting him, therefore he was already somewhat weakened. 2) After Shinryu is beaten, Estinian specifically says that the eyes are almost completely empty, which means Shinryu was almost to the point of disappearing -anyway-, so therefore we just shoved him over the edge.