Accomplish something in-game to recieve these different icons on your New Game/Continue screen. Getting them all will also result something new to appear on the screen. One will also be able to fight the Infinity Version of the Final Boss at the end of the game which has 4000 HP.

Unlockable - How to Unlock

Dragon Star - Defeat DragonSky
G Comp Star - Colllect all 5 Giga Cards
M Comp Star - Collect all 30 Mega Cards
Rockman [Megaman] Star - Finish the Main Story
S Comp Star - Collect all 150 Standard Cards
SP Comp Star - Obtain all SP Cards