@monsterhunter has tweeted some exciting news. You can now earn the Ryu costume in Monster Hunter: World if you have Street Fighter V save data on your system!
To get the quest for the materials to make the outfit, go to the gathering hub, and find the Arena Counter. Pick the quest called “Down the Dark, Muddy Path” under the section listed as Challenges.
It is a battle against the Brute Wyvern Barroth, and your character needs to be at lease Hunter Rank 3. Also, you must have a Street Fighter V save file on your system to access this quest, though Capcom reports that it will be out for everyone sometime soon.
To forge the Ryu armor, you need to go to the smith. It takes 7 “SFV Tickets”, 6 “Monster Bone M”, 6 “Earth Crystals”, and 5 “Barroth” shells. You’ll need to complete the arena quest a few times to get it all, as well as a bit of harvesting out in the game world. Once it’s done, you can set your Monster Hunter character to look like the fighting master that is Ryu.