Defeating Rio/Ryu
Run to the other side of the stage and jump up to the top platform. When Rio/Ryu runs over, jump behind him and use the Halo Bump attack. Then, go to the other side and repeat this tactic until you finish him off.
Defeating the second Boss
Go up close and slash him, or just get close to him. He should either attack you with his freeze punch then run, get on snowboard and attack you, or will use a bird freeze attack that launches iceballs at you. To counter the first one, run backward then attack. To counter the second attack, jump over the board two or three times then try to attack. To counter his third attack, move backward then slash the snowballs. Note: You will have to do this at least once during the attack. Also, when he gets on his board and ice spikes come out, you must run in the opposite direction.
Sword of Light
After defeating Eliza, go to the inn. You will get the Sword Of Light there. Ryu will say that he found it on the ground. You will also get a new Sprit Power called Celestial Slash. Note: You will not have Amidamru any more. When you use it, a little energy will come out.