You have to earn 250,000 Points by winning a duel against Pegasus at the Gate during the event. The amount of Points you gain is based on a Duel Assessment. For details, check the link to even details page above.
How to unlock Paradox Brothers
This special character can only be unlock whenever Paradox Brothers: Guardians of the Gate event is open.
Collect "Maze keys" by winning duels in the duel world (PVP, Casual, Gate duels excluded). Defeat the Paradox Brothers at gate during the event and earn points, earn 180,000 points to unlock the Paradox Brothers, this points are based on duel assessment, for more event details click the link above.
How to Unlock Yami Bakura
This Character can only be unlocked during the "Fear the Deck of Terror! The Destiny Board of Doom" event.