Some opponents can be unlocked by defeating them in Story mode five times. Complete the following tasks to unlock the remaining single duel opponents.

Alien Overlord: Buy all the center parts of the D Wheel.
Antique Gear Ultimate Golem: Summon Antique Gear Ultimate Golem.
Arcana Force EX - The Dark Ruler: Summon Arcana Force Ex - The Dark Ruler.
Barbaros: Accumulate 200 hours of game play.
Blue Eyes White Dragon: Summon Blue Eyes Ultimate Dragon.
Bryonac - Ice Dragon Boundary: Synchro Summon 200 times.
Colosal Fighter: Buy all the front parts of the D Wheel.
Dark Armed Dragon: Summon Armed Dragon Level 10.
Doom Dozer: Buy all the rear parts of the D Wheel.
Dragon D End: Summon D Hero Bloo-D.
E HERO Dark Gaia: Use 300 Speed Spell.
E HERO Hell Gainer: Accumulate 50 hours of game play.
Endymion: Win all single tournaments once each.
Exodios: Win using Exodios' effect.
Gladiator Beast Gyzarus: Summon Heraklinos.
Horus Level 8: Use magic card 750 times.
Jinzo Ningen - Psycho Lord: Use Trap card 500 times.
Judgment Dragon: Special Summon 1,000 times.
Light And Darkness Dragon: Accumulate 100 hours of game play.
Montage Dragon: Complete all five duel puzzles in Story mode.
Stardust Dragon/Assault Mode: Summon Stardust Dragon/Assault mode.
Ultimate Insect Level 7: Summon Perfect Ultimate Great Moth.
Venominaga: Summon Venominaga.
Yubel: Summon Yubel Das Extremer Traurig Drachen (third form).