You are exactly right. First Brain wave (which I love) is where I am dying.
First off, you should change the settings on the game to easy and give yourself 10 guys to start the game. This will give you ample time to practice on harder levels so you don't have to keep restarting the game. I'd try this for a while, then put the game on TG settings once you can score a few hundred grand.
You should not lose a life before the first brain wave. The waves leading up to it are all easy.
There are several strategies for the brain wave. Mostly I keep firing non-stop and go for as many humans as possible. On the first brain wave, there is a lone Mikey human. If you can keep him safe, the brains will not turn the other humans into Progs and you can grab more humans and score more points. Sometimes I will try to save him, but usually I will blast and grab on the brain levels. I've found that trying to save Mikely is rarely worth the risk and when I have, my score is rarely that much better and I have usually lost more lives doing it.
If there are a few humans left and one brain, I will go for the humans and not shoot the brain until the humans are saved. If you do a decent job on the brain wave, you should have around 100,000 points when it ends, and you will have lost 1 or 2 lives. Sometimes you can make it through the entire brain round without losing any, other times you can lose more, especially in the later brain waves.
In addition, you have to learn how to shoot the smart missiles that the brains are shooting. A good strategy is to learn to run away from them and keep firing at the missiles. You also needs to learn to shoot them head on. A lot of casual players just try to avoid the missiles but learning to shoot them is key to losing less lives on this level and scoring more points.
Another key on this game is learning to shoot diagonally in all directions.
Good luck.