The Mark of Mastery is an exam that keyblade wielders takes in order to become a true keyblade master. In the old records in Radiant Garden there are different forms of the Exam.
The first was to set two keyblade wielders against one another and the one to emerge victorious became the master. This occurs with Terra and Aqua in KHBbS.
If you want to choose this option then gather in Olympus Coliseum. Here you will be set against another character in a battle. Both characters may be eligible for Master status. This all depends on your roleplay battle.
The second form is of the exam is to travel around the worlds battling heartless and helping your fellow keyblade wielders Travelling would be done by use of the Star Shard, allowing for random teleportation. Mickey takes this exam under Master Yen Sid in KHBbs
If you choose this option, you will have to fight one of each type of enemy through the ages. One Unversed, One Heartless, and One Nobody. Nightmares are excluded since you would have to venture into the Dream Realms. Your qualification for Master will depend on your roleplay through the various challenges.
The third and final form is dream diving. The keyblade wielder dives into the dream worlds and must uncover the truth behind the past. This occurs in KH3Ds
If you choose this option then you will be transported to a world of sleep. There you will be confronted by a Nightmare or an enemy of the sleeping world. Your qualification for Master depends on your roleplay during the adventure.
Each Master will overlook one of the exams and the wielders taking them.
Gaint will overlook the first exam, Sensei will overlook the second exam, Sapphire will overlook the third exam.
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