Space Invaders have different types of levels. They're mostly the same, they only vary in difficulty and two players.
On the very left and right side there are regions which aren't possible to reach. So the enemies in the outer left side cannot be killed as first. They need to be killed at least as second. The enemies move faster if they got killed.
This table shows the probably fastest way to kill all enemies. The numbers are the periods in which the enemies are killed. Number 7 will move to the left.
2 1 3 4 5 7
2 1 3 4 5 7
2 1 3 4 5 6
2 1 3 4 5 6
2 1 3 4 5 6
2 1 3 4 5 6
This way is obviously slower. It also doesn't work due the fact that there is this area where enemies can't be hit.
7 6 6 6 6 7
5 5 5 5 5 5
4 4 4 4 4 4
3 3 3 3 3 3
2 2 2 2 2 2
1 1 1 1 1 1
Anyway, according to my calculations, a highest score run would take about 5 minutes.