If you shoot 20 guys in a row (without missing) on EASY mode you will get an extra life.
If you shoot 30 guys in a row on NORMAL mode you will get an extra life.
To unlock the extra time attack modes, you must first complete level one in Time Attack mode (ranking doesn't matter.)
Next, you must finish level two in the Time Attack mode and achieve first place in the ranking. This unlocks the color combo challenge, where the enemies' uniforms are changing colors, and by shooting multiple enemies of the same color consecutively increases your points.
Finally, finish level three in the Time Attack mode and again achieve first place in the ranking. You will unlock a harder version of the time attack mode, where you have very little time and must shoot the enemies as quickly as possible to earn more time.