Always try to get up close with your scouts, get behind cover, and use them multiple times to kill most of your enemies - just shoot 'em in the head, chances are very good you'll get at least 3 shots out of 5 at close range.
Use the Edelweiss to provide cover for your other soldiers... put it in such a position that it blocks enemy fire and lets you get to a safe place.
Once you get the orders "Damage boost" and "Demolition man" you can kill tanks by shooting them in the radiator with pretty much nay kind of soldier, not just a lancer. Imperial weapons help with that a lot as they do crazy damage to armor. works best with shocktroopers.
Before advancing anywhere, make use of snipers to take out any possible resistance along your way.
When enemies are behind cover, get their ass out of there by throwing a grenade at them. Even easier when you get elite scouts with grenade launchers.
Save your game at the start of each turn.
