Complete the indicated task to have the corresponding golden star appear at the title screen. After unlocking all five stars you can challenge Crimson Dragon SP.

Red Joker Star: Complete the game.
G Comp Star: Collect all the Giga cards.
M Comp Star: Collect all the Mega cards.
S Comp Star: Collect all the Standard cards.
SS Star: Defeat Sirius.

Complete the indicated task with a special wireless transmission to have the corresponding silver star appear at the title screen.

AJ Star: Defeat Acid Ace BB or Grave Joker RR.
Mu Star: Defeat Burai ZZ.
Sigma Star: Defeat Sirius Sigma, Moon Disaster Sigma, and Apollon Flame Sigma.