From what I can understand, it's all about maximizing your attacks. Up on the top screen, you have a small bar that says "attack". You can only store three sets of four enemies. If all four enemies in a set are the same color, you have a stronger attack.
For example, if you have the first set of enemies all red, the second set all green, and the third set half blue and half green, your attack will be pretty powerful, but not as much had the last set of four been all the same color.
Once you have all three sets of four filled up in your attack meter, any other kills you make will not count towards your attack, pretty much a waste. So make sure to shoot a UFO as close as possible to it being filled up. Killing one or two more after it's filled up and then killing a UFO to send the attack over is not too bad. But if you kill a wave of 30 enemies without hitting a UFO, you've pretty much wasted a whole line of attacks.
The other thing I've learned is it's not just about the amount or size of the attack, but constantly keeping pressure on the other side. Once you put a wave of enemies over, they keep proceeding down until the enemy kills them all. You'll notice your attack will stack on top of whatever wave of enemies is already on their side. If you send a wave over while they are still trying to kill the first wave, they are stacked on top still going down towards the enemy.
For example, if I send a full blown attack (three sets of four enemies) over to my enemy, then I wait for another full blown attack, they may have already squelched my first attack. So I want to send over waves to keep the pressure on them. I'll look at the top screen, and when they have maybe a handful of enemies to kill, I'll send more over to keep the attack coming because they stack one upon the other.
Now I'm not sure if the type of UFO you shoot makes a difference, but I'll see what I can find out.