To unlock characters in single duel mode, do the following:
Shimon: Defeat level 1 in Triple Duel.
Grandpa: Defeat level 1 in Triple Duel twice.
Yugi: Defeat level 6 or defeat level 1 in Triple Duel three times.
Tea: Defeat level 2 in Triple Duel.
Joey: Defeat level 10 or defeat level 2 in Triple Duel twice.
Tristan: Defeat level 2 in Triple Duel three times.
Bakura: Defeat level 3 in Triple Duel three times.
Shadi: Defeat level 3 in Triple Duel.
Yami Yugi: Defeat level 14, level 12 or level 3 in Triple Duel twice.
Weevil: Defeat level 4 in Triple Duel twice.
Rex Raptor: Defeat level 4 in Triple Duel.
Mako: Defeat level 4 in Triple Duel three times.
Bonz: Defeat level 5 in Triple Duel twice.
Bandit Keith: Defeat level 5 in Triple Duel three times.
Pegasus: Defeat level 5 in Triple Duel.
Mai: Defeat level 10 or level 6 in Triple Duel.
Kaiba: Defeat level 12 or level 6 in Triple Duel three times.
Rare Hunter: Defeat level 13 or level 7 in Triple Duel.
Arkana: Defeat level 7 twice in Triple Duel.
Strings: Defeat level 7 in Triple Duel three times.
Espa Roba: Defeat level 8 in Triple Duel twice.
Lumis and Umbra: Defeat level 8 in Triple Duel three times.
Marik: Defeat level 10 or level 8 in Triple Duel.
Ishizu: Defeat level 11 or level 9 in Triple Duel twice.
Odion: Defeat level 11 or level 9 in Triple Duel three times.
Yami Marik: Defeat level 14, level 12 or level 9 in Triple Duel.
Yami Bakura: Defeat level 14 or level 11 in Triple Duel.