The first fight with Kain is in Mount Ordeals after Kain enters the monument and his dark side arises. The fight is scripted and the player only has to survive a few turns. Jump is an excellent idea to make time to finish the battle.
The second fight takes place in the crystal room at Fabul where Kain is attempting to take the Crystal. It starts as a one-on-one battle between him and Ursula and the player can just attack normally, while using Chakra to heal. After a cutscene, Yang will join in the battle, and should use a cover counter on Ursula while she uses Chakra on Yang, but Ursula can still be hit by Jump. After the battle Kain jumps over them, takes the Wind Crystal, admits to acting of his own free will, and leaves.
Isn't this what you wanted all along!? You wanted Cecil dead...so you could have Rosa for yourself!
—Dark Kain against the Hooded Man
The third fight is in Baron Castle after Dark Kain kidnaps Rosa. The Hooded Man, who is the real Kain, fights him to settle their conflict. The fight is divided in two parts. At first the player can only survive a few rounds and a scene will occur where the Hooded Man's name changes to Kain and he learns the Jump ability. The player should use Jump a few times and heal with Hi-Potions. At the battles end Kain will turn into a Holy Dragoon.