To unlock the Ryu costume in Monster Hunter: World, have a Street Fighter 5 save file. The Ryu costume is tied to the "Down The Dark, Muddy Path" arena challenge in the Gathering Hub and is only available if you have played Street Fighter 5. This challenge puts you against a giant Barroth and can be completed with another player. This quest rewards you with SF5 tickets. You need seven tickets to unlock the Ryu costume.

You get the following number of tickets depending on your completion time:

Rank A (4 minutes): Three tickets
Rank B (8 minutes): Two tickets
Rank C (50 minutes): One ticket

After you have obtained seven SF5 tickets, go to Smithy's to unlock the Ryu costume. Additionally, you can still get the Ryu costume if you have not played Street Fighter 5 by joining into sessions that are focused on arena challenges. Go to a quest board and select "Search for an Online Session". Set the Quest preference to "Event Quests" to be paired with players that have the same goal.