To get Character's Signature Cards, beat them in Story Mode/Grand Prix

For example, beat Leo once in Story Mode to get Morphtronic Celfon. Beat him again to get Smashing Ground, and so on.

Unlockables

Bolt Tanner Beat Bolt Tanner in Stage 6-B
Burning Skull Head Beat Hunter Pace in Stage 6-A
Facility Chief's Duel Runner Beat Facility Chief in Stage 3
Greiger (Matchup Mode) Beat Greiger in Stage 7
Hoodlum's Duel Runner Beat Hoodlum in Stage 1
Hunter Pace (Matchup Mode) Beat Hunter Pace in Stage 6-A
Jack Atlas (Matchup Mode) Beat Story Mode twice
Leo's Duel Runner Beat Leo in Stage 2-A
Luna's Duel Runner Beat Luna in Stage 5-B
Mad Archfiend Beat Story Mode twice
Normal Duel Runner(Bolt Tanner's Duel Runner) Beat Bolt Tanner in Stage 6-B
Officer Tetsu Trudge (Matchup Mode) Beat Officer Tetsu Trudge in Stage 4
Officer Tetsu Trudge's Duel Runner Beat Officer Tetsu Trudge in Stage 4
Security 2's Duel Runner Beat the Silver Cup in 1st Place
Skull Collector Beat Hoodlum in Stage 1-A
Sparks Beat Greiger in Stage 7 a 2nd time
Stardust Dragon Beat Story Mode once
Summon Reactor-SK Beat Greiger in Stage 7
Sunlight Unicorn Beat Luna in Stage 5-B
Tremendous Fire Beat Hunter Pace in Stage 6-A a 2nd time
Ushi Oni Beat Bolt Tanner in Stage 6-B
Wall of Ivy Beat Akiza Stage 5-A
Wheel of Fortune (Jack Atlas' Duel Runner) Beat Story Mode twice
Yusei Fudo (Matchup Mode) Beat Story Mode once
Yusei's Duel Runner Beat Story Mode once