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.

Star Mark	How to unlock
G Comp Star	Beat all 5 Giga Cards
Leo Star	Defeat LeoKingdom
M Comp Star	Beat all 30 Mega Cards
Rockman [Megaman] Star	Finish the Main Story
S Comp Star	Beat all 150 Standard Cards
SP Comp Star	Obtain all SP Cards