Well first you join losla and u kill all the ninjas on her ship and afterwards ur outside dragon ki go in and watch the cutsecne and bing bang boom ur in.
Look at your adventure book on the Yokai storyline.
You can get the sword by defeating Kitsune(easier) or O-dokuru head(harder)!
when you get a invite for dragon koi tournamet you go to yoki and go to the first building you see and talk to the announcer and do the fights.
Invitational Tournament.